plan.md

Geometry and physics of black holes

These lectures introduce some aspects of black hole physics via a geometrical approach. The prerequisite is having some notions of general relativity, at the level of an introductory course.

Location

Space: Amphitheatre Henri Mineur, IAP, Paris

Time: Schedule (IAP page)

Lecture 1 (11 March 2016)

Introduction and general framework

• Spacetime manifold
• Worldlines of particles and observers
• Energy, momentum and frequency as measured by an observer
• Einstein equation

The concept of black hole 1: Horizons and null hypersurfaces

• Null hypersurfaces as causal boundaries
• Geometry of null hypersurfaces
• Non-expanding horizons
• Killing horizons

Lecture 2 (18 March 2016)

The concept of black hole 2: The global view

• Conformal completion
• General definition of a black hole

The Schwarzschild black hole

• The Schwarzschild-(A)dS solution
• The Kruskal-Szekeres diagram
• The Einstein-Rosen bridge
• Geodesics and ray-tracing in the Schwarzschild spacetime

Lecture 3 (25 March 2016)

The Kerr black hole

• The Kerr solution in different coordinate systems
• The Cauchy horizon and the ring singularity
• Geodesics and ray-tracing in the Kerr spacetime
• The ergoregion and the Penrose process

Lecture 4 (1 April 2016)

Evolution and thermodynamics of black holes

• The four laws of black hole dynamics
• Gravitational collapse
• Penrose singularity theorem

Black holes and gravitational waves

• Quasi-normal modes of Kerr black holes
• Maximum energy radiated in gravitational waves
• Binary black hole mergers

Lecture 5 (8 April 2016)

The quasi-local approach: trapping horizons

• Trapping horizons and dynamical horizons
• Evolution laws and the viscous fluid analogy
• Thermodynamics

Lecture 6 (14 April 2016)

Higher-dimensional solutions and black holes in alternative theories

• Schwarzschild-Tangherlini solution
• Myers-Perry black holes
• Black rings
• Black holes in Lovelock theories
• Einstein-Gauss-Bonnet black holes