# 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)