These pages accompany Éric Gourgoulhon's lectures in the framework of the PSL Graduate Program in Physics, organized by the Doctoral School Physique en Île-de-France (ED 564), from 30 April to 11 June 2025.
These lectures are devoted to various aspects of black hole physics, which are relevant both for contemporary astrophysics and for fundamental physics. The prerequisite is having followed an introductory course of general relativity, typically at the level of a master's degree. Doctorate students should register here.
The lectures are taking place in room CONF IV = E244 of the ENS Physics Department, 24 rue Lhomond, 75005 Paris.
Lectures 1 and 2 set the theoretical framework and discuss the basic properties of black holes. In particular, the concept of Killing horizon (Lecture 2) is central in the theory of stationary black holes. Lectures 3 and 4 are quite relevant for astrophysics, since, by virtue of the no-hair theorem, all isolated and stationary black holes in the Universe are expected to be Kerr black holes. Notably Lecture 4 is devoted to the interpretation of the images of M87* and Sgr A* recently obtained by the Event Horizon Telescope. On the other side, Lectures 5 to 7 are more theoretically oriented. In particular, black hole thermodynamics is pivotal in the current approaches to quantum gravity. Keeping in mind applications to theoretical physics, the spacetime dimension n is kept general, except in Lectures 3 and 4, where n=4 is assumed. Similarly, it will be made clear whether a given result is valid only in general relativity (i.e. relies on the Einstein equation) or remains true in modified theories of gravity.
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