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402-0830-00L 10 Credits BSC , MSC D-PHYS , D-MATH
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General Relativity

Lecturers & Examiners: Prof. Dr. Gian Michele Graf
VVZ CR n/a

Last Updated: 2026-02-05 15:24:13

Abstract

Manifolds, Lie derivatives, connections, curvature, metric; Equivalence principle, postulates of General Relativity; Energy-momentum tensor, field equations, Newtonian gravity as limit, cosmological constant, Hilbert action; Friedmann cosmologies, astrophysical observations; Schwarzschild-Kruskal metric, classical tests, black holes, Kerr metric, Hawking radiation; gravitational waves, radiation

Content

1. Differentiable manifolds (vector fields, tensor fields, Lie derivative, covariant derivative, torsion and curvature) 2. Pseudo-riemannian manifolds (metric, Levi-Civita connection, geodesics, normal coordinates) 3. Space, time and gravitation (Einstein equivalence principle, postulates of GR, physical laws in the external gravitational field, gravitational redshift, free fall and its Newtonian limit) 4. The Einstein field equation (Energy-momentum tensor, dust and ideal fluids, Newtonian gravity, cosmological constant, Einstein-Hilbert action) 5. The homogeneous, isotropic universe (Friedmann models, cosmological redshift, astrophysical observations) 6. Black holes (stationary and static metrics, the Schwarzschild solution, geodesics: perihelion precession and light deflection, the Kruskal extension, the Kerr-Newman family) 7. The weak field limit (the linearized theory of gravity, gauges, gravitational waves, polarizations, radiation and quadrupole formula, application: radiation of binary systems) Further topics as time permits.

Resources

Literature

Suggested textbooks: S. Carroll: An introduction to General Relativity Spacetime and Geometry B. Schutz: A first course in general relativity N. Straumann: General relativity with applications to astrophysics R. Wald: General Relativity C. Misner, K, Thorne and J. Wheeler: Gravitation J. Hartle: Gravity: an introduction to general relativity

General Information

Language
English
Levels
BSC , MSC
Frequency
Yearly recurring

Examination

Type
session examination
Mode
oral 30 minutes

Course Components

Type Title Time & Place Hours
lecture General Relativity
  • Tue 14:45-16:30 (HPV G 5)
  • Thu 08:45-10:30 (HCI J 6)
4 h weekly
exercise General Relativity
  • Wed 10:45-11:30 (HPK D 24.2)
  • Fri 12:45-13:30 (HIT J 53)
1 h weekly

Offered In