General Relativity & Quantum Cosmology

Black holes: Dark stars, Rindler space analogy, Kruskal extension, Astrophysical BHs

Schwarzschild metric: Birkhoff's theorem, Singularities, Geodesics, Mercury perihelion shift

Gravitational waves: guest speaker Luis Lehner, Landau's pseudotensor, Energy loss due to GWs

Gravitational waves: gauge fixing, 2 polarizations, quadrupole formula

Einstein equations, Bianchi identity, Conservation laws, Energy conditions, Linearized gravity

Energy-momentum conservation, Born-Infeld theory, Einstein-Hilbert action, Lovelock theorem

Particles and matter in curved spacetime, Geodesic deviation equation, Energy momentum tensor

Killing vectors, Curvature, Riemann family, Bianchi identity & Einstein tensor

Covariant derivative, Metric, Equivalence principle, Invariant volume element, Parallel transport

Tensors, Tensor algebra, Differentiating tensors, Connection

Gravitational redshift again, Field theory for gravity, Manifolds