PSI 2018/2019 - Gravitational Physics Review (Gregory)

Review of differential geometry: manifolds, tensors, differential forms

Lie derivative and symmetries, Killing vectors, ON basis

Cartan's formalism: connection & curvature

Spherically symmetric spacetimes, Schwarzschild-(A)dS black holes

Black holes, horizons, and causal structure

Rotating black holes and black hole thermodynamics

Gravitational action: Palatini lemma, Gauss-Codazzi formalism, Gibbons-Hawking term

Calculation of Euclidean action & black hole entropy, Israel equations

Physical submanifolds: domain walls & cosmic strings

Kaluza-Klein theory, KK black holes

Black branes: higher-dimensional Schwarzschild, p-form charges, D3 branes, black string instability

Warped compactifications: Rubakov-Shaposhnikov & Randall-Sundrum toy models