Relativistic Mechanics

This is a course of the master program in MpM.
We spend sometimes to set a common background.
The main goal of the course is to obtain exact Kepler laws in general relativity for a material point moving in a Schwarzschild gravitational field.

Lecture 1: Video  (1:33:24)
What is a manifold?
Rough definition, charts, coordinates, transition functions
Spacetime
Observers

Lecture 2: Video (1:22:53)
What is a metric?
What is a connection?
Gravitational field
Geodesics

Lecture 3: Video (1:35:09)
Lagrangian mechanics
The Lagrangian for geodesics

Lecture 4: Video (1:23:42)
Second Kepler laws
Third Kepler laws
Motion of light and deflection angle

Lecture 5: Video (1:20:49)
Kepler with Maple

Lecture 6: Video (1:12:50)
light rays with Maple

Lecture 7: Video (0:58:58)
Synchronization surfaces, observers and time.

Extra background: 
• What is a metric (0:54:12)
• Connections (0:36:57)
• Parallel transport (0:54:35)