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		<id>http://universeinproblems.com/index.php?action=history&amp;feed=atom&amp;title=Category%3AHorizons</id>
		<title>Category:Horizons - Revision history</title>
		<link rel="self" type="application/atom+xml" href="http://universeinproblems.com/index.php?action=history&amp;feed=atom&amp;title=Category%3AHorizons"/>
		<link rel="alternate" type="text/html" href="http://universeinproblems.com/index.php?title=Category:Horizons&amp;action=history"/>
		<updated>2026-04-05T23:01:55Z</updated>
		<subtitle>Revision history for this page on the wiki</subtitle>
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	<entry>
		<id>http://universeinproblems.com/index.php?title=Category:Horizons&amp;diff=2051&amp;oldid=prev</id>
		<title>Cosmo All at 09:32, 23 April 2014</title>
		<link rel="alternate" type="text/html" href="http://universeinproblems.com/index.php?title=Category:Horizons&amp;diff=2051&amp;oldid=prev"/>
				<updated>2014-04-23T09:32:19Z</updated>
		
		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table class='diff diff-contentalign-left'&gt;
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				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 09:32, 23 April 2014&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l1&quot; &gt;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;In this chapter we assemble the problems that concern one of the most distinctive features of General Relativity and Cosmology &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;--&lt;/del&gt;- the horizons. The first part gives an elementary introduction into the concept in the cosmological context, following and borrowing heavily from the most comprehensible text by E. Harrison &amp;lt;ref name=Harrison /&amp;gt;. Then we move to more formal exposition of the subject, making use of the seminal works of W. Rindler&amp;lt;ref name=Rindler /&amp;gt; and G.F.R. Ellis, T. Rothman&amp;lt;ref name=Ellis /&amp;gt;, and consider first simple, and then composite models, such as $\Lambda$CDM. The fourth section elevates the rigor one more step and explores the causal structure of different simple cosmological models in terms of conformal diagrams, following mostly the efficient approach of V. Mukhanov&amp;lt;ref name=Mukhanov /&amp;gt;, and inflation. The section on black holes relates the general scheme of constructing conformal diagrams for stationary black hole spacetimes, following mostly the excellent textbook of K. Bronnikov and S. Rubin&amp;lt;ref name=BrRubin /&amp;gt;. The consequent sections focus on more specific topics, such as the various problems regarding the Hubble sphere, inflation and holography.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;In this chapter we assemble the problems that concern one of the most distinctive features of General Relativity and Cosmology - the horizons. The first part gives an elementary introduction into the concept in the cosmological context, following and borrowing heavily from the most comprehensible text by E. Harrison &amp;lt;ref name=Harrison /&amp;gt;. Then we move to more formal exposition of the subject, making use of the seminal works of W. Rindler&amp;lt;ref name=Rindler /&amp;gt; and G.F.R. Ellis, T. Rothman&amp;lt;ref name=Ellis /&amp;gt;, and consider first simple, and then composite models, such as $\Lambda$CDM. The fourth section elevates the rigor one more step and explores the causal structure of different simple cosmological models in terms of conformal diagrams, following mostly the efficient approach of V. Mukhanov&amp;lt;ref name=Mukhanov /&amp;gt;, and inflation. The section on black holes relates the general scheme of constructing conformal diagrams for stationary black hole spacetimes, following mostly the excellent textbook of K. Bronnikov and S. Rubin&amp;lt;ref name=BrRubin /&amp;gt;. The consequent sections focus on more specific topics, such as the various problems regarding the Hubble sphere, inflation and holography.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==References==&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==References==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Cosmo All</name></author>	</entry>

	<entry>
		<id>http://universeinproblems.com/index.php?title=Category:Horizons&amp;diff=1707&amp;oldid=prev</id>
		<title>Igor: /* References */</title>
		<link rel="alternate" type="text/html" href="http://universeinproblems.com/index.php?title=Category:Horizons&amp;diff=1707&amp;oldid=prev"/>
				<updated>2013-10-31T08:39:12Z</updated>
		
		<summary type="html">&lt;p&gt;‎&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;References&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table class='diff diff-contentalign-left'&gt;
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				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 08:39, 31 October 2013&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l3&quot; &gt;Line 3:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 3:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==References==&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==References==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;references&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;references&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;ref name=Harrison&amp;gt;E. Harrison. Cosmology: the science of the Universe. CUP (1981)&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;ref name=Harrison&amp;gt;E. Harrison. Cosmology: the science of the Universe. CUP (1981) &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;ISBN 978-0-521-66148-5&lt;/ins&gt;&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;ref name=&amp;quot;Rindler&amp;quot;&amp;gt;W. Rindler. Visual horizons in world-models. [http://adsabs.harvard.edu/abs/1956MNRAS.116..662R MNRAS 116 (6), 662--677 (1956) (1981)]&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;ref name=&amp;quot;Rindler&amp;quot;&amp;gt;W. Rindler. Visual horizons in world-models. [http://adsabs.harvard.edu/abs/1956MNRAS.116..662R MNRAS 116 (6), 662--677 (1956) (1981)]&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;ref name=&amp;quot;Ellis&amp;quot;&amp;gt;G.F.R. Ellis and T. Rothman. Lost horizons. Am. J. Phys. 61, 883 (1993)&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;ref name=&amp;quot;Ellis&amp;quot;&amp;gt;G.F.R. Ellis and T. Rothman. Lost horizons. Am. J. Phys. 61, 883 (1993)&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Igor</name></author>	</entry>

	<entry>
		<id>http://universeinproblems.com/index.php?title=Category:Horizons&amp;diff=1706&amp;oldid=prev</id>
		<title>Igor: /* References */</title>
		<link rel="alternate" type="text/html" href="http://universeinproblems.com/index.php?title=Category:Horizons&amp;diff=1706&amp;oldid=prev"/>
				<updated>2013-10-31T08:36:29Z</updated>
		
		<summary type="html">&lt;p&gt;‎&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;References&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table class='diff diff-contentalign-left'&gt;
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				&lt;col class='diff-content' /&gt;
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				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 08:36, 31 October 2013&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l6&quot; &gt;Line 6:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 6:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;ref name=&amp;quot;Rindler&amp;quot;&amp;gt;W. Rindler. Visual horizons in world-models. [http://adsabs.harvard.edu/abs/1956MNRAS.116..662R MNRAS 116 (6), 662--677 (1956) (1981)]&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;ref name=&amp;quot;Rindler&amp;quot;&amp;gt;W. Rindler. Visual horizons in world-models. [http://adsabs.harvard.edu/abs/1956MNRAS.116..662R MNRAS 116 (6), 662--677 (1956) (1981)]&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;ref name=&amp;quot;Ellis&amp;quot;&amp;gt;G.F.R. Ellis and T. Rothman. Lost horizons. Am. J. Phys. 61, 883 (1993)&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;ref name=&amp;quot;Ellis&amp;quot;&amp;gt;G.F.R. Ellis and T. Rothman. Lost horizons. Am. J. Phys. 61, 883 (1993)&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;ref name=&amp;quot;Mukhanov&amp;quot;&amp;gt;V.F. Mukhanov. Physical foundations of cosmology (CUP, 2005) ISBN&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;~&lt;/del&gt;0521563984&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;ref name=&amp;quot;Mukhanov&amp;quot;&amp;gt;V.F. Mukhanov. Physical foundations of cosmology (CUP, 2005) ISBN 0521563984&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;ref name=&amp;quot;BrRubin&amp;quot;&amp;gt;K.A. Bronnikov and S.G. Rubin. Black Holes, Cosmology and Extra Dimensions. (WSPC, 2012), ISBN&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;~&lt;/del&gt;978-9814374200&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;ref name=&amp;quot;BrRubin&amp;quot;&amp;gt;K.A. Bronnikov and S.G. Rubin. Black Holes, Cosmology and Extra Dimensions. (WSPC, 2012), ISBN 978-9814374200&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;!-- &amp;lt;ref name=&amp;quot;Melia&amp;quot;&amp;gt;F. Melia. The cosmic horizon.&amp;#160; MNRAS 382 (4), 1917--1921 (2007) [http://arxiv.org/abs/0711.4181 arXiv:0711.4181];&amp;lt;br/&amp;gt;F. Melia and M. Abdelqader, The Cosmological Spacetime,&amp;#160; Int. J. Mod. Phys. D 18, 1889 (2009) [http://arxiv.org/abs/0907.5394 arXiv:0907.5394]&amp;lt;/ref&amp;gt; --&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;!-- &amp;lt;ref name=&amp;quot;Melia&amp;quot;&amp;gt;F. Melia. The cosmic horizon.&amp;#160; MNRAS 382 (4), 1917--1921 (2007) [http://arxiv.org/abs/0711.4181 arXiv:0711.4181];&amp;lt;br/&amp;gt;F. Melia and M. Abdelqader, The Cosmological Spacetime,&amp;#160; Int. J. Mod. Phys. D 18, 1889 (2009) [http://arxiv.org/abs/0907.5394 arXiv:0907.5394]&amp;lt;/ref&amp;gt; --&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;/references&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;/references&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Igor</name></author>	</entry>

	<entry>
		<id>http://universeinproblems.com/index.php?title=Category:Horizons&amp;diff=1699&amp;oldid=prev</id>
		<title>Igor at 20:26, 7 October 2013</title>
		<link rel="alternate" type="text/html" href="http://universeinproblems.com/index.php?title=Category:Horizons&amp;diff=1699&amp;oldid=prev"/>
				<updated>2013-10-07T20:26:24Z</updated>
		
		<summary type="html">&lt;p&gt;&lt;/p&gt;
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				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 20:26, 7 October 2013&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l1&quot; &gt;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;In this chapter we assemble the problems that concern one of the most distinctive features of General Relativity and Cosmology --- the horizons. The first part gives an elementary introduction into the concept in the cosmological context, following and borrowing heavily from the most comprehensible text by E. Harrison &amp;lt;ref name=Harrison /&amp;gt;. Then we move to more formal exposition of the subject, making use of the seminal works of W. Rindler&amp;lt;ref name=Rindler /&amp;gt; and G.F.R. Ellis, T. Rothman&amp;lt;ref name=Ellis /&amp;gt;, and consider first simple, and then composite models, such as $\Lambda$CDM. The fourth section elevates the rigor one more step and explores the causal structure of different simple cosmological models in terms of conformal diagrams, following mostly the efficient approach of V. Mukhanov&amp;lt;ref name=Mukhanov /&amp;gt;&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;. &lt;/del&gt;and inflation. The section on black holes relates the general scheme of constructing conformal diagrams for stationary black hole spacetimes, following mostly the excellent textbook of K. Bronnikov and S. Rubin&amp;lt;ref name=BrRubin /&amp;gt;. The consequent sections focus on more specific topics, such as the various problems regarding the Hubble sphere, inflation and holography.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;In this chapter we assemble the problems that concern one of the most distinctive features of General Relativity and Cosmology --- the horizons. The first part gives an elementary introduction into the concept in the cosmological context, following and borrowing heavily from the most comprehensible text by E. Harrison &amp;lt;ref name=Harrison /&amp;gt;. Then we move to more formal exposition of the subject, making use of the seminal works of W. Rindler&amp;lt;ref name=Rindler /&amp;gt; and G.F.R. Ellis, T. Rothman&amp;lt;ref name=Ellis /&amp;gt;, and consider first simple, and then composite models, such as $\Lambda$CDM. The fourth section elevates the rigor one more step and explores the causal structure of different simple cosmological models in terms of conformal diagrams, following mostly the efficient approach of V. Mukhanov&amp;lt;ref name=Mukhanov /&amp;gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;, &lt;/ins&gt;and inflation. The section on black holes relates the general scheme of constructing conformal diagrams for stationary black hole spacetimes, following mostly the excellent textbook of K. Bronnikov and S. Rubin&amp;lt;ref name=BrRubin /&amp;gt;. The consequent sections focus on more specific topics, such as the various problems regarding the Hubble sphere, inflation and holography.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==References==&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==References==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Igor</name></author>	</entry>

	<entry>
		<id>http://universeinproblems.com/index.php?title=Category:Horizons&amp;diff=1698&amp;oldid=prev</id>
		<title>Igor at 20:25, 7 October 2013</title>
		<link rel="alternate" type="text/html" href="http://universeinproblems.com/index.php?title=Category:Horizons&amp;diff=1698&amp;oldid=prev"/>
				<updated>2013-10-07T20:25:50Z</updated>
		
		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table class='diff diff-contentalign-left'&gt;
				&lt;col class='diff-marker' /&gt;
				&lt;col class='diff-content' /&gt;
				&lt;col class='diff-marker' /&gt;
				&lt;col class='diff-content' /&gt;
				&lt;tr style='vertical-align: top;' lang='en'&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 20:25, 7 October 2013&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l1&quot; &gt;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;In this chapter we assemble the problems that concern one of the most distinctive features of General Relativity and Cosmology --- the horizons. The first part gives an elementary introduction into the concept in the cosmological context, following and borrowing heavily from the most comprehensible text by E. Harrison &amp;lt;ref name=Harrison /&amp;gt;. Then we move to more formal exposition of the subject, making use of the seminal works of W. Rindler&amp;lt;ref name=Rindler /&amp;gt; and G.F.R. Ellis, T. Rothman&amp;lt;ref name=Ellis /&amp;gt;, and consider first simple, and then composite models, such as $\Lambda$CDM. The fourth section elevates the rigor one more step and explores the causal structure of different simple cosmological models in terms of conformal diagrams, following mostly the efficient approach of V. Mukhanov&amp;lt;ref name=&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;Muchanov &lt;/del&gt;/&amp;gt;. and inflation. The section on black holes relates the general scheme of constructing conformal diagrams for stationary black hole spacetimes, following mostly the excellent textbook of K. Bronnikov and S. Rubin&amp;lt;ref name=BrRubin /&amp;gt;. The consequent sections focus on more specific topics, such as the various problems regarding the Hubble sphere, inflation and holography.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;In this chapter we assemble the problems that concern one of the most distinctive features of General Relativity and Cosmology --- the horizons. The first part gives an elementary introduction into the concept in the cosmological context, following and borrowing heavily from the most comprehensible text by E. Harrison &amp;lt;ref name=Harrison /&amp;gt;. Then we move to more formal exposition of the subject, making use of the seminal works of W. Rindler&amp;lt;ref name=Rindler /&amp;gt; and G.F.R. Ellis, T. Rothman&amp;lt;ref name=Ellis /&amp;gt;, and consider first simple, and then composite models, such as $\Lambda$CDM. The fourth section elevates the rigor one more step and explores the causal structure of different simple cosmological models in terms of conformal diagrams, following mostly the efficient approach of V. Mukhanov&amp;lt;ref name=&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;Mukhanov &lt;/ins&gt;/&amp;gt;. and inflation. The section on black holes relates the general scheme of constructing conformal diagrams for stationary black hole spacetimes, following mostly the excellent textbook of K. Bronnikov and S. Rubin&amp;lt;ref name=BrRubin /&amp;gt;. The consequent sections focus on more specific topics, such as the various problems regarding the Hubble sphere, inflation and holography.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==References==&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==References==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Igor</name></author>	</entry>

	<entry>
		<id>http://universeinproblems.com/index.php?title=Category:Horizons&amp;diff=1697&amp;oldid=prev</id>
		<title>Igor at 20:25, 7 October 2013</title>
		<link rel="alternate" type="text/html" href="http://universeinproblems.com/index.php?title=Category:Horizons&amp;diff=1697&amp;oldid=prev"/>
				<updated>2013-10-07T20:25:30Z</updated>
		
		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table class='diff diff-contentalign-left'&gt;
				&lt;col class='diff-marker' /&gt;
				&lt;col class='diff-content' /&gt;
				&lt;col class='diff-marker' /&gt;
				&lt;col class='diff-content' /&gt;
				&lt;tr style='vertical-align: top;' lang='en'&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 20:25, 7 October 2013&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l6&quot; &gt;Line 6:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 6:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;ref name=&amp;quot;Rindler&amp;quot;&amp;gt;W. Rindler. Visual horizons in world-models. [http://adsabs.harvard.edu/abs/1956MNRAS.116..662R MNRAS 116 (6), 662--677 (1956) (1981)]&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;ref name=&amp;quot;Rindler&amp;quot;&amp;gt;W. Rindler. Visual horizons in world-models. [http://adsabs.harvard.edu/abs/1956MNRAS.116..662R MNRAS 116 (6), 662--677 (1956) (1981)]&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;ref name=&amp;quot;Ellis&amp;quot;&amp;gt;G.F.R. Ellis and T. Rothman. Lost horizons. Am. J. Phys. 61, 883 (1993)&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;ref name=&amp;quot;Ellis&amp;quot;&amp;gt;G.F.R. Ellis and T. Rothman. Lost horizons. Am. J. Phys. 61, 883 (1993)&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;ref name=&amp;quot;&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;Muchanov&lt;/del&gt;&amp;quot;&amp;gt;V.F. &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;Muchanov&lt;/del&gt;. Physical foundations of cosmology (CUP, 2005) ISBN~0521563984&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;ref name=&amp;quot;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;Mukhanov&lt;/ins&gt;&amp;quot;&amp;gt;V.F. &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;Mukhanov&lt;/ins&gt;. Physical foundations of cosmology (CUP, 2005) ISBN~0521563984&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;ref name=&amp;quot;BrRubin&amp;quot;&amp;gt;K.A. Bronnikov and S.G. Rubin. Black Holes, Cosmology and Extra Dimensions. (WSPC, 2012), ISBN~978-9814374200&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;ref name=&amp;quot;BrRubin&amp;quot;&amp;gt;K.A. Bronnikov and S.G. Rubin. Black Holes, Cosmology and Extra Dimensions. (WSPC, 2012), ISBN~978-9814374200&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;ref name=&amp;quot;Melia&amp;quot;&amp;gt;F. Melia. The cosmic horizon.&amp;#160; MNRAS 382 (4), 1917--1921 (2007) [http://arxiv.org/abs/0711.4181 arXiv:0711.4181];&amp;lt;br/&amp;gt;F. Melia and M. Abdelqader, The Cosmological Spacetime,&amp;#160; Int. J. Mod. Phys. D 18, 1889 (2009) [http://arxiv.org/abs/0907.5394 arXiv:0907.5394]&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;lt;!-- &lt;/ins&gt;&amp;lt;ref name=&amp;quot;Melia&amp;quot;&amp;gt;F. Melia. The cosmic horizon.&amp;#160; MNRAS 382 (4), 1917--1921 (2007) [http://arxiv.org/abs/0711.4181 arXiv:0711.4181];&amp;lt;br/&amp;gt;F. Melia and M. Abdelqader, The Cosmological Spacetime,&amp;#160; Int. J. Mod. Phys. D 18, 1889 (2009) [http://arxiv.org/abs/0907.5394 arXiv:0907.5394]&amp;lt;/ref&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;gt; --&lt;/ins&gt;&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;/references&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;/references&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Igor</name></author>	</entry>

	<entry>
		<id>http://universeinproblems.com/index.php?title=Category:Horizons&amp;diff=1670&amp;oldid=prev</id>
		<title>Cosmo All at 07:00, 29 September 2013</title>
		<link rel="alternate" type="text/html" href="http://universeinproblems.com/index.php?title=Category:Horizons&amp;diff=1670&amp;oldid=prev"/>
				<updated>2013-09-29T07:00:09Z</updated>
		
		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table class='diff diff-contentalign-left'&gt;
				&lt;col class='diff-marker' /&gt;
				&lt;col class='diff-content' /&gt;
				&lt;col class='diff-marker' /&gt;
				&lt;col class='diff-content' /&gt;
				&lt;tr style='vertical-align: top;' lang='en'&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 07:00, 29 September 2013&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l1&quot; &gt;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;In this chapter we assemble the problems that concern one of the most distinctive features of General Relativity and Cosmology --- the horizons. The first part gives an elementary introduction into the concept in the cosmological context, following and borrowing heavily from the most comprehensible text by E. Harrison &amp;lt;ref name=Harrison /&amp;gt;. Then we move to more formal exposition of the subject, making use of the seminal works of W. Rindler&amp;lt;ref name=Rindler /&amp;gt; and G.F.R. Ellis, T. Rothman&amp;lt;ref name=Ellis /&amp;gt;. The &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;third &lt;/del&gt;section elevates the rigor one more step and explores the causal structure of different simple cosmological models in terms of conformal diagrams, following mostly the efficient approach of V. Mukhanov&amp;lt;ref name=Muchanov /&amp;gt;. &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;The following sections focus on more specific topics, such as the various problems regarding the Hubble sphere&amp;lt;ref name=Melia /&amp;gt;, more realistic composite models (including $\Lambda$CDM), &lt;/del&gt;and inflation. The section on black holes relates the general scheme of constructing conformal diagrams for stationary black hole spacetimes, following mostly the excellent textbook of K. Bronnikov and S. Rubin&amp;lt;ref name=BrRubin /&amp;gt;.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;In this chapter we assemble the problems that concern one of the most distinctive features of General Relativity and Cosmology --- the horizons. The first part gives an elementary introduction into the concept in the cosmological context, following and borrowing heavily from the most comprehensible text by E. Harrison &amp;lt;ref name=Harrison /&amp;gt;. Then we move to more formal exposition of the subject, making use of the seminal works of W. Rindler&amp;lt;ref name=Rindler /&amp;gt; and G.F.R. Ellis, T. Rothman&amp;lt;ref name=Ellis /&amp;gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;, and consider first simple, and then composite models, such as $\Lambda$CDM&lt;/ins&gt;. The &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;fourth &lt;/ins&gt;section elevates the rigor one more step and explores the causal structure of different simple cosmological models in terms of conformal diagrams, following mostly the efficient approach of V. Mukhanov&amp;lt;ref name=Muchanov /&amp;gt;. and inflation. The section on black holes relates the general scheme of constructing conformal diagrams for stationary black hole spacetimes, following mostly the excellent textbook of K. Bronnikov and S. Rubin&amp;lt;ref name=BrRubin /&amp;gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;. The consequent sections focus on more specific topics, such as the various problems regarding the Hubble sphere, inflation and holography&lt;/ins&gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==References==&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==References==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Cosmo All</name></author>	</entry>

	<entry>
		<id>http://universeinproblems.com/index.php?title=Category:Horizons&amp;diff=1669&amp;oldid=prev</id>
		<title>Igor at 11:04, 26 September 2013</title>
		<link rel="alternate" type="text/html" href="http://universeinproblems.com/index.php?title=Category:Horizons&amp;diff=1669&amp;oldid=prev"/>
				<updated>2013-09-26T11:04:21Z</updated>
		
		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table class='diff diff-contentalign-left'&gt;
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				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 11:04, 26 September 2013&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l1&quot; &gt;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;In this chapter we assemble the problems that concern one of the most distinctive features of General Relativity and Cosmology --- the horizons. The first part gives an elementary introduction into the concept in the cosmological context, following and borrowing heavily from the most comprehensible text by E. Harrison &amp;lt;ref name=Harrison /&amp;gt;. Then we move to more formal exposition of the subject, making use of the seminal works of W. Rindler&amp;lt;ref name=Rindler /&amp;gt; and G.F.R. Ellis, T. Rothman&amp;lt;ref name=Ellis /&amp;gt;. The third section elevates the rigor one more step and explores the causal structure of different simple cosmological models in terms of conformal diagrams, following mostly the efficient approach of V. Mukhanov&amp;lt;ref name=Muchanov /&amp;gt;. The following sections focus on more specific topics, such as the various problems regarding the Hubble sphere, more realistic composite models (including $\Lambda$CDM), and inflation. The section on black holes relates the general scheme of constructing conformal diagrams for stationary black hole spacetimes, following mostly the excellent textbook of K. Bronnikov and S. Rubin&amp;lt;ref name=BrRubin /&amp;gt;.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;In this chapter we assemble the problems that concern one of the most distinctive features of General Relativity and Cosmology --- the horizons. The first part gives an elementary introduction into the concept in the cosmological context, following and borrowing heavily from the most comprehensible text by E. Harrison &amp;lt;ref name=Harrison /&amp;gt;. Then we move to more formal exposition of the subject, making use of the seminal works of W. Rindler&amp;lt;ref name=Rindler /&amp;gt; and G.F.R. Ellis, T. Rothman&amp;lt;ref name=Ellis /&amp;gt;. The third section elevates the rigor one more step and explores the causal structure of different simple cosmological models in terms of conformal diagrams, following mostly the efficient approach of V. Mukhanov&amp;lt;ref name=Muchanov /&amp;gt;. The following sections focus on more specific topics, such as the various problems regarding the Hubble sphere&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;lt;ref name=Melia /&amp;gt;&lt;/ins&gt;, more realistic composite models (including $\Lambda$CDM), and inflation. The section on black holes relates the general scheme of constructing conformal diagrams for stationary black hole spacetimes, following mostly the excellent textbook of K. Bronnikov and S. Rubin&amp;lt;ref name=BrRubin /&amp;gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==References==&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==References==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;references&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;references&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;ref name=Harrison&amp;gt;E. Harrison. Cosmology: the science of the Universe. CUP (1981)&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;ref name=Harrison&amp;gt;E. Harrison. Cosmology: the science of the Universe. CUP (1981)&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;ref name=&amp;quot;Rindler&amp;quot;&amp;gt;W. Rindler. Visual horizons in world-models. MNRAS 116 (6), 662--677 (1956) (1981)&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;ref name=&amp;quot;Rindler&amp;quot;&amp;gt;W. Rindler. Visual horizons in world-models. &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;[http://adsabs.harvard.edu/abs/1956MNRAS.116..662R &lt;/ins&gt;MNRAS 116 (6), 662--677 (1956) (1981)&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;]&lt;/ins&gt;&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;ref name=&amp;quot;Ellis&amp;quot;&amp;gt;G.F.R. Ellis and T. Rothman. Lost horizons. Am. J. Phys. 61, 883 (1993)&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;ref name=&amp;quot;Ellis&amp;quot;&amp;gt;G.F.R. Ellis and T. Rothman. Lost horizons. Am. J. Phys. 61, 883 (1993)&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;ref name=&amp;quot;Muchanov&amp;quot;&amp;gt;V.F. Muchanov. Physical foundations of cosmology (CUP, 2005) ISBN~0521563984&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;ref name=&amp;quot;Muchanov&amp;quot;&amp;gt;V.F. Muchanov. Physical foundations of cosmology (CUP, 2005) ISBN~0521563984&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;ref name=&amp;quot;BrRubin&amp;quot;&amp;gt;K.A. Bronnikov and S.G. Rubin. Black Holes, Cosmology and Extra Dimensions. (WSPC, 2012), ISBN~978-9814374200&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;ref name=&amp;quot;BrRubin&amp;quot;&amp;gt;K.A. Bronnikov and S.G. Rubin. Black Holes, Cosmology and Extra Dimensions. (WSPC, 2012), ISBN~978-9814374200&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;ref name=&amp;quot;Melia&amp;quot;&amp;gt;F. Melia. The cosmic horizon.&amp;#160; MNRAS 382 (4), 1917--1921 (2007) [http://arxiv.org/abs/0711.4181 arXiv:0711.4181];&amp;lt;br/&amp;gt;F.&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;~&lt;/del&gt;Melia and M.&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;~&lt;/del&gt;Abdelqader, The Cosmological Spacetime,&amp;#160; Int. J. Mod. Phys. D 18, 1889 (2009) [http://arxiv.org/abs/0907.5394 arXiv:0907.5394]&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;ref name=&amp;quot;Melia&amp;quot;&amp;gt;F. Melia. The cosmic horizon.&amp;#160; MNRAS 382 (4), 1917--1921 (2007) [http://arxiv.org/abs/0711.4181 arXiv:0711.4181];&amp;lt;br/&amp;gt;F. Melia and M. Abdelqader, The Cosmological Spacetime,&amp;#160; Int. J. Mod. Phys. D 18, 1889 (2009) [http://arxiv.org/abs/0907.5394 arXiv:0907.5394]&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;/references&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;/references&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Igor</name></author>	</entry>

	<entry>
		<id>http://universeinproblems.com/index.php?title=Category:Horizons&amp;diff=1664&amp;oldid=prev</id>
		<title>Cosmo All at 21:35, 25 September 2013</title>
		<link rel="alternate" type="text/html" href="http://universeinproblems.com/index.php?title=Category:Horizons&amp;diff=1664&amp;oldid=prev"/>
				<updated>2013-09-25T21:35:52Z</updated>
		
		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table class='diff diff-contentalign-left'&gt;
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				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 21:35, 25 September 2013&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l2&quot; &gt;Line 2:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 2:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==References==&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==References==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;{{reflist|refs=&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;lt;references&amp;gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;ref name=Harrison&amp;gt;E. Harrison. Cosmology: the science of the Universe. CUP (1981)&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;ref name=Harrison&amp;gt;E. Harrison. Cosmology: the science of the Universe. CUP (1981)&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;ref name=&amp;quot;Rindler&amp;quot;&amp;gt;W. Rindler. Visual horizons in world-models. MNRAS 116 (6), 662--677 (1956) (1981)&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;ref name=&amp;quot;Rindler&amp;quot;&amp;gt;W. Rindler. Visual horizons in world-models. MNRAS 116 (6), 662--677 (1956) (1981)&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l9&quot; &gt;Line 9:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 9:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;ref name=&amp;quot;BrRubin&amp;quot;&amp;gt;K.A. Bronnikov and S.G. Rubin. Black Holes, Cosmology and Extra Dimensions. (WSPC, 2012), ISBN~978-9814374200&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;ref name=&amp;quot;BrRubin&amp;quot;&amp;gt;K.A. Bronnikov and S.G. Rubin. Black Holes, Cosmology and Extra Dimensions. (WSPC, 2012), ISBN~978-9814374200&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;ref name=&amp;quot;Melia&amp;quot;&amp;gt;F. Melia. The cosmic horizon.&amp;#160; MNRAS 382 (4), 1917--1921 (2007) [http://arxiv.org/abs/0711.4181 arXiv:0711.4181];&amp;lt;br/&amp;gt;F.~Melia and M.~Abdelqader, The Cosmological Spacetime,&amp;#160; Int. J. Mod. Phys. D 18, 1889 (2009) [http://arxiv.org/abs/0907.5394 arXiv:0907.5394]&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;ref name=&amp;quot;Melia&amp;quot;&amp;gt;F. Melia. The cosmic horizon.&amp;#160; MNRAS 382 (4), 1917--1921 (2007) [http://arxiv.org/abs/0711.4181 arXiv:0711.4181];&amp;lt;br/&amp;gt;F.~Melia and M.~Abdelqader, The Cosmological Spacetime,&amp;#160; Int. J. Mod. Phys. D 18, 1889 (2009) [http://arxiv.org/abs/0907.5394 arXiv:0907.5394]&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;}}&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;lt;/references&amp;gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Cosmo All</name></author>	</entry>

	<entry>
		<id>http://universeinproblems.com/index.php?title=Category:Horizons&amp;diff=1663&amp;oldid=prev</id>
		<title>Cosmo All at 12:40, 25 September 2013</title>
		<link rel="alternate" type="text/html" href="http://universeinproblems.com/index.php?title=Category:Horizons&amp;diff=1663&amp;oldid=prev"/>
				<updated>2013-09-25T12:40:25Z</updated>
		
		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table class='diff diff-contentalign-left'&gt;
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				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 12:40, 25 September 2013&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l1&quot; &gt;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;In this chapter we assemble the problems that concern one of the most distinctive features of General Relativity and Cosmology --- the horizons. The first part gives an elementary introduction into the concept in the cosmological context, following and borrowing heavily from the most comprehensible text by E. Harrison &amp;lt;ref name=Harrison /&amp;gt;. Then we move to more formal exposition of the subject, making use of the seminal works of W. Rindler &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;\cite{&lt;/del&gt;Rindler&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;} &lt;/del&gt;and G.F.R. Ellis, T. Rothman &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;\cite{&lt;/del&gt;Ellis&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;}&lt;/del&gt;. The third section elevates the rigor one more step and explores the causal structure of different simple cosmological models in terms of conformal diagrams, following mostly the efficient approach of V. Mukhanov &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;\cite{&lt;/del&gt;Muchanov&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;}&lt;/del&gt;. The following sections focus on more specific topics, such as the various problems regarding the Hubble sphere, more realistic composite models (including $\Lambda$CDM), and inflation. The section on black holes relates the general scheme of constructing conformal diagrams for stationary black hole spacetimes, following mostly the excellent textbook of K. Bronnikov and S. Rubin &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;\cite{&lt;/del&gt;BrRubin&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;}&lt;/del&gt;.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;In this chapter we assemble the problems that concern one of the most distinctive features of General Relativity and Cosmology --- the horizons. The first part gives an elementary introduction into the concept in the cosmological context, following and borrowing heavily from the most comprehensible text by E. Harrison &amp;lt;ref name=Harrison /&amp;gt;. Then we move to more formal exposition of the subject, making use of the seminal works of W. Rindler&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;lt;ref name=&lt;/ins&gt;Rindler &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;/&amp;gt; &lt;/ins&gt;and G.F.R. Ellis, T. Rothman&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;lt;ref name=&lt;/ins&gt;Ellis &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;/&amp;gt;&lt;/ins&gt;. The third section elevates the rigor one more step and explores the causal structure of different simple cosmological models in terms of conformal diagrams, following mostly the efficient approach of V. Mukhanov&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;lt;ref name=&lt;/ins&gt;Muchanov &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;/&amp;gt;&lt;/ins&gt;. The following sections focus on more specific topics, such as the various problems regarding the Hubble sphere, more realistic composite models (including $\Lambda$CDM), and inflation. The section on black holes relates the general scheme of constructing conformal diagrams for stationary black hole spacetimes, following mostly the excellent textbook of K. Bronnikov and S. Rubin&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;lt;ref name=&lt;/ins&gt;BrRubin &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;/&amp;gt;&lt;/ins&gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==References==&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==References==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Cosmo All</name></author>	</entry>

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