General Relativity

The course requires solid knowledge of physics, calculus and algebra taught during the first two years of study. Required courses: Fizyka I, Fizyka II, Fizyka III, Mechanika klasyczna, Analiza I, Analiza II, Analiza III, Algebra z geometrią I, Algebra z geometrią II. Not required but helpful courses: Elektrodynamika, Geometria różniczkowa, Teoria grup w fizyce.

w sali

Course plan:

1. Euclidean and Minkowski spaces.

2. Basics of differential geometry.

3. Formulation of General Relativity.

4. Weak gravitational fields.

5. Schwarzschild spacetime.

6. The simplest cosmological models.

1. Euclidean and Minkowski spaces:

affine spaces, affine spaces equipped with a scalar product.

2. Basics of differential geometry:

tensor calculus, differentiable manifolds, tensor fields, metrics, Lie derivative, covariant derivative, Riemann tensor, parallel transport, Killing vector fields.

3. Formulation of General Relativity:

basic concepts, postulates of GR, Einstein's equation.

4. Weak gravitational fields:

linearized Einstein's equation, Newtonian limit of GR, linear gravitational waves.

5. Schwarzschild spacetime:

static spherically symmetric spacetime, Schwarzschild metric, free test particles in the Schwarzschild spacetime, Kruskal-Szekeres extention, Schwarzschild black hole.

6. The simplest cosmological models

spatially homogeneous and isotropic spacetime, Robertson-Walker metrics, models with dust and radiation, Hubble law

1. Robert M. Wald "General Relativity";

2. Charles W. Misner, Kip S. Thorne, John A. Wheeler "Gravitation";

3. Bernard F. Schutz "A first course in general relativity".

Rules of passing the course:

1. attendance at 38 hours of the lecture or the classes or both;

2. passing the examination, which will consist of a written and an oral part.