Summary

The course aims to introduce and develop physical understanding of relativistic gravitational physics.

Course subjects:

0. Introduction: What is relativistic gravity

1. Review of basic ideas and calculational tools
a. The metric tensor
b. The covariant derivative
c. Tensors and their properties
d. Curvature
e. The geodesic equation
f. The geodesic deviation equation

2. Einstein's equations
a. The gravitational action
b. Einstein's equations in vacuum
c. The matter action
d. Einstein's equations with sources
e. Conservation of the energy-momentum tensor

3. Gravitational waves in flat space-time
a. Einstein's equations in the weak field expansion
b. The gauge freedom and gauge fixing
c. Solving Einstein's equations: the two polarizations of gravitational waves
d. The influence of gravitational waves on matter
e. Einstein's equations with sources in the weak field expansion
f. A quadropole source: orders of magnitude and estimates
g. (astro) physical sources of gravitational waves
h. Direct and indirect detection of gravitational waves
i. Gravitational waves astronomy

4. Black holes
a. The Schwarzschild geometry and Birkhoff's theorem
b. Gravitational collapse and black holes
c. Killing vectors of the Schwarzschild geometry
d. Geodesics equations and their solutions
e. Orbits of point particles and light near black holes
f. The redshift
g. The event horizon
h. Analytical continuation beyond the horizon and the Kruskal geometry
i. Conformal maps, Penrose coordinates and Penrose diagrams
j. Charged black holes
k. Rotating black holes
l. The laws of black holes
m. Thermodynamics of black holes

5. The Universe
a. Introduction to the Universe, dark matter
b. The size of the universe, mapping the universe
c. The expanding Universe, the redshift
d. The accelerated expansion of the universe, dark energy
e. Cosmological observations
f. Homogeneous and isotropic models of the Universe
g. The Robertson-Walker metric
h. Models of matter, perfect fluid, cold matter, ra