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| − | = Dynamics of Universe in Problems = | + | = Dynamics of the Universe in Problems = |
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| + | === I. About === | ||
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| + | There are about 500 websites on the Internet with names that contain the term “cosmology”. Many of them are devoted to discussion of fundamental questions: whether there is life on Mars, what was there when there was nothing and the like. Our aim is much more modest. We present here an online living version of our book of problems on cosmology. | ||
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| + | === II. Why problems, which and for whom?=== | ||
| + | The only way to rise above the “popular” level in any science is to master its alphabet, that is, to learn to solve problems, even if most simple at the beginning. To our best knowledge, there are no problem books on cosmology yet, that would include its spectacular recent achievements. Of course, most of excellent modern textbooks on cosmology include problems. However, a reader, exhausted by high theory, may often be thwarted by the lack of time and strength to solve them. | ||
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| + | You can familiarize oneself with the modern portrayal of the dynamics of the Universe, including the latest achievements of cosmology, by solving problems from the start. The perseverant will traverse the thorny path of cosmology’s evolution from the traditional Big Bang model to the presently universally accepted Standard Cosmological Model. It is based on the revolutionary discovery of accelerated expansion of the Universe, made at the very end of the last century. The attempts to explain such an unexpected observation led to fundamental reconstruction of the view on the evolution of the Universe that was formed in the XX century. | ||
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| + | One only has to be acquainted with the basics of Special and General Relativities and the theory of elementary particles in order to start solving problems. We want to show that even this minimal knowledge is sufficient to be able to solve a very wide range of cosmological problems, and moreover, to understand the essence of difficulties that are encountered by modern cosmology. | ||
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| + | No generation of Homo sapiens could withstand the temptation to claim that the true understanding of the nature of the Universe is (almost?) within its grasp. The current generation is not an exception, of course, naturally assuming it has better reason to believe so than ever before. We hope to give our reader the means to evaluate objectively whether this is true or not by himself. | ||
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| + | === III. Second life online=== | ||
| + | We published the first edition of the problem book a couple of years ago, in Russian. However, a printed book, even not taking into account the language, has its obvious drawbacks in itself. The audience is limited by the number of copies printed. The inevitable misprints and errors cannot be corrected – the errors in classical problem books on physics are known to be sometimes corrected in the fifteenth edition. But the main problem that almost immediately manifested itself was that the content of the book with pretentious title “Modern Cosmology” was getting out of date by leaps and bounds. New sections and subsections demanded to be created and populated with problems. The online living problem book is the solution we have come to. | ||
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| + | At the moment we have about 1500 problems, almost all of them with solutions, and we hope to bring them online by the fall of 2012. We tried to make references to the authors of problems whenever possible and would be happy to add the references that might still be missing. Some problems have already acquired the status of folklore and their authorship is hard to determine. We welcome all comments, suggestions and corrections to the formulations of problems and their solutions, but most valuable to us would be new problems suggested by the community. | ||
| + | |||
| + | === IV. Good luck=== | ||
| + | Finally, we hope that after getting to grip with the problems our reader not only preserves his interest to cosmology, but tries to make the next step: read original papers. If this transition is overcome seamlessly, we will have achieved our goal. | ||
| + | |||
| + | Welcome! | ||
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Revision as of 12:05, 27 June 2012
Contents
Dynamics of the Universe in Problems
I. About
There are about 500 websites on the Internet with names that contain the term “cosmology”. Many of them are devoted to discussion of fundamental questions: whether there is life on Mars, what was there when there was nothing and the like. Our aim is much more modest. We present here an online living version of our book of problems on cosmology.
II. Why problems, which and for whom?
The only way to rise above the “popular” level in any science is to master its alphabet, that is, to learn to solve problems, even if most simple at the beginning. To our best knowledge, there are no problem books on cosmology yet, that would include its spectacular recent achievements. Of course, most of excellent modern textbooks on cosmology include problems. However, a reader, exhausted by high theory, may often be thwarted by the lack of time and strength to solve them.
You can familiarize oneself with the modern portrayal of the dynamics of the Universe, including the latest achievements of cosmology, by solving problems from the start. The perseverant will traverse the thorny path of cosmology’s evolution from the traditional Big Bang model to the presently universally accepted Standard Cosmological Model. It is based on the revolutionary discovery of accelerated expansion of the Universe, made at the very end of the last century. The attempts to explain such an unexpected observation led to fundamental reconstruction of the view on the evolution of the Universe that was formed in the XX century.
One only has to be acquainted with the basics of Special and General Relativities and the theory of elementary particles in order to start solving problems. We want to show that even this minimal knowledge is sufficient to be able to solve a very wide range of cosmological problems, and moreover, to understand the essence of difficulties that are encountered by modern cosmology.
No generation of Homo sapiens could withstand the temptation to claim that the true understanding of the nature of the Universe is (almost?) within its grasp. The current generation is not an exception, of course, naturally assuming it has better reason to believe so than ever before. We hope to give our reader the means to evaluate objectively whether this is true or not by himself.
III. Second life online
We published the first edition of the problem book a couple of years ago, in Russian. However, a printed book, even not taking into account the language, has its obvious drawbacks in itself. The audience is limited by the number of copies printed. The inevitable misprints and errors cannot be corrected – the errors in classical problem books on physics are known to be sometimes corrected in the fifteenth edition. But the main problem that almost immediately manifested itself was that the content of the book with pretentious title “Modern Cosmology” was getting out of date by leaps and bounds. New sections and subsections demanded to be created and populated with problems. The online living problem book is the solution we have come to.
At the moment we have about 1500 problems, almost all of them with solutions, and we hope to bring them online by the fall of 2012. We tried to make references to the authors of problems whenever possible and would be happy to add the references that might still be missing. Some problems have already acquired the status of folklore and their authorship is hard to determine. We welcome all comments, suggestions and corrections to the formulations of problems and their solutions, but most valuable to us would be new problems suggested by the community.
IV. Good luck
Finally, we hope that after getting to grip with the problems our reader not only preserves his interest to cosmology, but tries to make the next step: read original papers. If this transition is overcome seamlessly, we will have achieved our goal.
Welcome!
CONTENT
1.1 Astronomy "before the Common Era" 1.2 Quantities large and small 1.3 Geometric warm-up 1.4 Planck scales and fundamental constants $c$, $G$, $\hbar$ 1.5 Gravity 1.6 Forest for the trees 1.7 Life on Mars? 1.7.1 Fine-tuning of the Universe 1.8 Thermo warm-up
2. Dynamics of the Expanding Universe
2.1 Homogeneous and isotropic Universe, Hubble's Law 2.2 Equations of General Relativity 2.3 Friedman-Lemaitre-Robertson-Walker (FLRW) metric 2.4 Expanding Universe: ordinarity, difficulties and paradoxes 2.4.1 Warm-up 2.4.2 The tethered galaxy problem 2.4.3 Cosmological redshift 2.5 Friedman equations 2.6 Newtonian cosmology 2.7 Energy balance in an expanding Universe 2.8 Cosmography
3. Dynamics of the Universe in the Big Bang Model
3.1 General questions 3.2 Solutions of Friedman equations in the Big Bang model 3.3 The role of curvature in the dynamics of the Universe 3.4 The Milne Universe 3.5 Cosmological horizons 3.6 Energy conditions and the Raychaudhuri equation 3.6.1 Energy conditions 3.6.2 Raychaudhuri equation 3.6.2 Sudden future singularities 3.7 Influence of cosmological expansion on local systems 3.8 Dynamics of the Universe in terms of redshift and conformal time
4. Black Holes
4.1 Technical warm-up 4.1.1 Uniformly accelerated observer, Rindler metric 4.1.2 Metric in curved spacetime 4.2 Schwarzschild black hole 4.2.1 Simple problems 4.2.2 Symmetries and integrals of motion 4.2.3 Radial motion 4.2.4 Blackness of black holes 4.2.5 Orbital motion, effective potential 4.2.6 Miscellaneous problems 4.2.7 Different coordinates, maximal extension 4.3 Kerr black hole 4.3.1 General axially symmetric metric 4.3.2 Limiting cases 4.3.3 Horizons and singularity 4.3.4 Stationary limit 4.3.5 Ergosphere and the Penrose process 4.3.6 Integrals of motion 4.3.7 The laws of mechanics of black holes 4.3.8 Particles' motion in the equatorial plane 4.4 Astrophysical black holes 4.4.1 Preliminary 4.4.2 Quantum effects
