BGU Physics Department

Gravitation II

(3 points, 4 hours)

course number 203-2-4191

Links

• Course information
• Main web page

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• Introduction: What is relativistic gravity
• Review of basic ideas and calculational tools
  • The metric tensor
  • The covariant derivative
  • Tensors and their properties
  • Curvature
  • The geodesic equation
  • The geodesic deviation equation
• Einstein's equations
  • The gravitational action
  • Einstein's equations in vacuum
  • The matter action
  • Einstein's equations with sources
  • Conservation of the energy-momentum tensor
• Gravitational waves in flat space-time
  • Einstein's equations in the weak field expansion
  • The gauge freedom and gauge fixing
  • Solving Einstein's equations: the two polarizations of gravitationan waves
  • The influence of gravitational waves on matter
  • Einstein's equations with sources in the weak field expansion
  • A quadropole source: orders of magnitude and estimates
  • (astro) physical sources of  gravitational waves
  • Direct and indirect detection of gravitational waves
  • Gravitational waves astronomy
• Black holes
  • The Schwarzschild geometry and Birkhoff's theorem
  • Gravitational collapse and black holes
  • Killing vectors of the Schwarzschild geometry
  • Geodesics equations and their solutions
  • Orbits of point particles and light near black holes
  • The redshift
  • The event horizon
  • Analytical continuation beyond the horizon and the Kruskal geometry
  • Conformal maps, Penrose coordinates and Penrose diagrams
  • Charged black holes
  • Rotating black holes
  • The laws of black holes
  • Thermodynamics of black holes
• The Universe
  • Introduction to the Universe,  dark matter
  • The size of the universe, mapping the universe
  • The expanding Universe, the redshift
  • The accelerated expansion of the universe, dark energy
  • Cosmological observations
  • Homogeneous and isotropic models of the Universe
  • The Robertson-Walker metric
  • Models of matter, perfect fluid, cold matter, radiation and the cosmological constant
  • The Friedmann-Robertson-Walker model
  • The big bang
  • Cosmic inflation
  • The history of the universe

Sources

1. Gravitation, by Kip S. Thorne, Charles W. Misner, John Archibald Wheeler, Kip Thorne, John Wheeler
2. Gravitation and Cosmology : Principles and Applications of the General Theory of Relativity, Steven Weinberg
3. Spacetime and Geometry: An Introduction to General Relativity, Sean Carroll
4. P.K. Townsend, Black Holes: Lecture Notes
5. Was Einstein Right ?, Clifford M. Will
6. Introducing Einstein's Relativity, Ray D'Inverno
7. General Relativity, Robert M. Wald
8. Gravity: An Introduction to Einstein's General Relativity, James B. Hartle
9. Living Review
10. A First Course in General Relativity, Bernard F. Schutz
11. Hawking, S.W,  Ellis, G.F. R , Large Scale Structure Of Space-Time
12. G. 't Hooft, Introduction to General Relativity.

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