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
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) :