This course provides a graduate-level introduction to General Relativity and its applications to Relativistic Astrophysics. It will introduce the basic mathematical concepts of Lorentzian manifolds, discuss physics in external gravitational fields, and introduce Einstein’s field equations. The theory will be applied to Relativistic Astrophysics and discuss applications such as black hole solutions, neutron stars, and the generation of gravitational waves. Interested B.Sc. students are welcome.
Contents
1. Prelude: Newton's theory of gravity and the road to General Relativity
2. Mathematical foundations: manifolds, vector and tensor fields, Lorentzian manifolds, covariant derivative, geodesics and parallel transport, curvature
3. Equivalence principle and physics in curved spacetime
4. Einstein’s field equations
5. First applications: The Schwarzschild solution, Birkhoff’s theorem, neutron stars, gravitational waves |
