Objectives:

Detailed knowledge of General Relativity and its applications in Cosmology.

skills:
. Competence in analysis and synthesis;
. Knowledge of a foreign language;
. Competence to solve problems;
. Competence in critical thinking;
. Competence in independent learning;
. Use the internet as a means of communication and source of information;
. Group work in competence;
. creativity;
. Competence to apply in practice the theoretical knowledge;
. Competence to investigate;

Geometry and Gravitation - historic introduction. Non-Euclidean geometries and theories of gravitation.
Special Relativity - Revision.
Concepts of relativistic hydrodynamics. Momentum-energy tensor of a perfect fluid: properties, conservation laws. Fundamental equations.
The equivalence principle. The Eötvös-Dicke e de Pound- Rebka experiments. Affine connection and metric tensor. Christoffel symbols.
The principle of general covariance and its implications.
Gravitation and space curvature. Riemann-Christoffel and Ricci tensors, curvature scalar. Parallel transport and curvature tensor. Bianchi identities.
Einstein equation in a quasi-minkowski metric.
Solutions of Einstein equations for isostatic and isotropic fields; singularity,
General equation of motion of a particle or photon in a gravitational field. Applications.
Cosmological principle. Red shift. Robertson-Walker metric. Models. Big-Bang, evolution of the universe.

Basic knowledge of special relativity