course number 203-2-4191

- 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

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

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