This is a course in general relativity and the theory of the gravitational field. The student is expected to familiarise with the basic notion of general relativity and to be able to autonomously derive some of its classical results of astrophysical interest such as the precession of the perielio, the deflection of the light and the gravitational collapse of a sphere of dust.
Course Prerequisites
Linear algebra. Newtonian Physics. Classical electromagnetism. Special relativity.
Teaching Methods
Blackboard lectures
Assessment Methods
Homework Exercises at the blackboard
Contents
Summary of special Relativity 0.1 Relativistic Invariance of the interval 0.2 the Minkowski space-time 0.3 Lorentz transformations 0.4 Non inertial reference systems The gravitational field 1.1 The principles of equivalence 1.2 Curvilinear coordinates 1.3 Distances and time intervals 1.4 Covariant derivation 1.5 Christoffel symbols of and the metric tensor 1.6 Motion of a particle 1.7 Constant gravitational field Equations of the gravitational field 2.1 Riemann Tensor 2.2 Properties of the tensor 2.3 The action principle 2.4 The energy-momentum tensor 2.5 Einstein’s equations 2.6 The Newton law Gravity of massive bodies 3.1 Central symmetry 3.2 Trajectories in the Schwarzschild field 3.2.1 Precession of the perihelion 3.2.2 Gravitational deflection of light Black holes 4.1 Kruskal coordinates 4.2 Kerr’s solution 4.3 Gravitational collapse of a sphere of dust Stars 5.1 TOV equation 5.2 Chandrasekar Limit Gravitational waves Cosmology
Course Language
English
More information
Oral examination Exercises at the blackboard Theoretical questions.
