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.
Bibliography of reference
B. F. Schutz, A first course in general relativity, CUP 1990
H. Stephani, General Relativity. An introduction to the theory of the gravitational field, CUP 1990
J. B. Hartle, Gravity: an introduction to Einstein General Relativity, Addison-Wesley 2003
S. Carrol, Lectures on General Relativity, http://xxx.lanl.gov/abs/gr-qc/9712019
S. Weinberg, Gravitation and Cosmology, John Wiley & Sons 1972
S. Weinberg, Cosmology, CUP 2008
C. W. Misner, K. S. Thorne, J. A. Wheeler, Gravitation, W. H. Freeman & Co Ltd 1973
L. Ryder, Introduction to General Relativity, CUP 2009