Geometry and physics of black holes
IAP Advanced Lectures
Paris, March-April 2016
These lectures introduce some aspects of black hole physics via a geometrical approach. The prerequisite is to have 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 as null hypersurfaces
- Null hypersurfaces as causal boundaries
- Geometry of null hypersurfaces
[Video]
Lecture 2 (18 March 2016)
The concept of black hole 1: Horizons as null hypersurfaces (cont'd)
- Non-expanding horizons
- Killing horizons
The concept of black hole 2: The global view
- Conformal completion of Minkowski spacetime
[Video]
Lecture 3 (25 March 2016)
The concept of black hole 2: The global view (cont'd)
- Conformal completions and asymptotic flatness
- Black holes: general definition
- Properties of the event horizon
[Video]
Lecture 4 (1 April 2016)
The concept of black hole 2: The global view (cont'd)
- Stationary black holes
- No-hair theorem
The Schwarzschild black hole
- The Schwarzschild solution
- Eddington-Finkelstein coordinates
- The Kruskal-Szekeres diagram
- The Einstein-Rosen bridge
[Video]
Lecture 5 (8 April 2016)
The Kerr black hole
- The Kerr solution
- 3+1 Kerr coordinates
- The Cauchy horizon and the ring singularity
- The ergoregion and the Penrose process
Evolution and thermodynamics of black holes
- The four laws of black hole dynamics
[Video]
Lecture 6 (14 April 2016)
Bifurcate Killing horizons
- Expressions of the surface gravity
- Completeness of null generators of a Killing horizon
- Bifurcation surface
Maximal extension of Kerr spacetime
The quasi-local approach: trapping horizons
- Trapped surfaces
- Penrose singularity theorem
- Apparent horizons
- Future-outer trapping horizons
- Dynamical horizons
Gravitational collapse: the Vaidya example
- The Vaidya solution
- Event and trapping horizons in Vaidya spacetime
[Video]
Another time...
Geodesics and ray-tracing in black hole spacetimes
- Null and timelike geodesics of Kerr spacetime
- The Gyoto code
Black holes and gravitational waves
- Maximum energy radiated in gravitational waves
- Quasi-normal modes of Kerr black holes
- Binary black hole mergers
More on the quasi-local approach
- Evolution laws and the viscous fluid analogy
- Thermodynamics
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