*)N.B. if there are students who do not speak Portuguese the language is English.
Detailed knowledge of General Relativity and its applications in Cosmology.
. 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;
. 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
Generic skills to reach
. Competence in analysis and synthesis; . Knowledge of a foreign language; . Competence to solve problems; . Critical thinking; . Competence in autonomous learning; . Using the internet as a communication medium and information source; . Competence for working in group; . Creativity; . Competence in applying theoretical knowledge in practice; . Research skills; (by decreasing order of importance)
Teaching hours per semester
total of teaching hours
Sseminar or study visit
Laboratory or field work
Synthesis work thesis
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
Expository teaching with constant references to physical systems whose description fits the equations presented. Emphasis will be given to the mathematical techniques necessary for the understanding of the theory.