Revision as of 07:08, 17 June 2012

Dynamics of Universe in Problems

To our best knowledge, there are no problem books on cosmology yet, that would include its spectacular recent achievements. We believe there is a strong need for such now, when cosmology is swiftly becoming a strict and vast science, and the book would be extremely useful for the youth pouring in this area of research. Indeed, the only way to rise over the popular level in any science is to master its alphabet, that is, to learn to solve problems. Of course, most of 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. Might it be worth sometimes to change the tactics and just throw those who wish to learn to swim into the water?

The proposed problems constitute our contribution to this cause. There are over 1000 problems, divided into 14 chapters, covering topics from the dynamics of the expanding Universe and CMB to cosmology beyond the Lambda-CDM model and holography. We intend to publish their solutions in later editions. The reader, however, is encouraged to look for answers independently, even though – or especially so because – the problems range from easy to not quite and from elements of scientific folklore already to those with answers not quite settled.

CONTENT

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 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

3. Black Holes

  3.1 Technical warm-up
  
      3.1.1 Uniformly accelerated observer, Rindler metric
  
      3.1.2 Metric in curved spacetime
  
  3.2 Schwarzschild black hole
  
      3.2.1 Simple problems
  
      3.2.2 Symmetries and integrals of motion of Schwarzschild metric
  
      3.2.3 Radial motion in Schwarzschild metric
  
      3.2.4 Blackness of black holes
  
      3.2.5 Orbital motion, effective potential
  
      3.2.6 Miscellaneous problems
  
      3.2.7 Different coordinates, maximal extension
  
  3.3 Kerr black hole
  
      3.3.1 General axially symmetric metric
  
      3.3.2 Limiting cases
  
      3.3.3 Horizons and singularity
  
      3.3.4 Stationary limit
  
      3.3.5 Ergosphere and the Penrose process
  
      3.3.6 Integrals of motion
  
      3.3.7 The laws of mechanics of black holes
  
      3.3.8 Particles' motion in the equatorial plane   
  
  3.4 Astrophysical black holes
  
      3.4.1 Preliminary
  
      3.4.2 Quantum effects