General Relativity and Cosmology

Recommended Prerequisites

Basic knowledge of special relativity.

Teaching Methods

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.

Learning Outcomes

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.

Work Placement(s)

No

Syllabus

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.

Head Lecturer(s)

João Pedro Trancoso Gomes Rosa

Assessment Methods

Assessment
Synthesis work: 30.0%
Mini Tests: 70.0%

Bibliography

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