Nathalie Deruelle, General Relativity : A Primer

Lecture 1. Monday, September 18th, 14:30-17:30

Lecture 2. Tuesday, September 19th, 14:30-17:30

Lecture 3. Wednesday, September 20th, 14:30-17:30

Lecture 4. Thursday, September 21th, 14:30-17:30

Lecture 5. Friday, September 22th, 14:30-17:30

Lecture 6. Monday, September 25th, 14:30-17:30

Plan and PDF notes

Newtonian space-time

Non-linear coordinates and covariant derivative

Newtonian inertial and gravitational forces

Newtonian “cosmology” and the problem of propagation of light

Special Relativity in inertial frames

General covariance and accelerated frames

Inertial forces and gravity: spacetime is curved

Part 2. Einstein’s gravitational ﬁeld equations

Introduction to the Riemann tensor

Differential geometry and the curvature tensor

Cartan’s equations of structure

Metric manifolds

Motion of matter in a gravitational ﬁeld

Einstein’s ﬁeld equations

Isometries and symmetric spacetimes

Part 3. Relativistic stars, gravitational collapse and black holes

Newtonian star models

The Schwarzschild solution

Relativistic star models

Gravitational collapse Schwarzschild black hole

Charged black holes

The Kerr solution

Part 4. Weak gravitational ﬁelds

Schwarzschild solution and the classical tests

Motion of spinning particles

Gravitational waves

The problem of moving charges in electromagnetism

The problem of moving masses in General Relativity

PSR 1913+16

Notes of the master course given at Ecole Normale Supérieure (Paris) :

- Special Relativity
- General Relativity
- Cosmology
- Relativistic stars and black holes
- Gravitational waves and relativistic celestial mechanics