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Introduction to General Relativity (WS21/22)


Prof. Dr. Stefan Dittmaier and Dr. Maximilian Stahlhofen


  • Lecture: 4 hours, Thu 10-12 (Seminaraum I), Fri 14-16 (Hörsaal I), start: 21.10.2021

  • Tutorial: 2 hours, Mon 14-16 (Seminarraum I)
    Exception: The first tutorial session will take place on Tue, Nov 2, 2pm, since Nov 1 is a holiday.

ILIAS link

To get access to the ILIAS page please register for the lecture in HISinOne. Your registration will be transferred to ILIAS automatically (usually over night).


  • Special relativity and its limitations:
    kinematics, dynamics, electrodynamics, gravitation and limits of special relativity

  • Basics of differential geometry:
    differentiable manifolds, vectors and tangent space, one-forms and cotangent space, tensors, differential forms and exterior differentiation, volume form and integration, parallel transport and covariant derivative, curvature and torsion, metric and Riemannian connection, Killing vectors

  • Gravitation:
    basic concept, space-time geometry, physics in curved space-time, Lagrangian formalism, energy-momentum tensor, electromagnetism, Einstein’s equation, cosmological constant

  • Schwarzschild solution and black holes:
    Schwarzschild metric, geodesics of the Schwarzschild metric, classical experimental tests, black holes

  • Cosmology:
    Robertson-Walker metrics, Friedmann equation, cosmological evolution

  • Perturbation theory and gravitational waves:
    linearized gravity, gravitational waves


Theoretical Mechanics, Electrodynamics, and Special Relativity


  • S. N. Carroll, “Spacetime and Geometry: An Introduction to General Relativity”, Cambridge University Press, 2019
  • T. Frankel, “The Geometry of Physics: An Introduction”, Cambridge University Press, 2011
  • L. D. Landau, J. M. Lifschitz, Lehrbuch der theoretischen Physik, Band 2, “Klassische Feldtheorie”, Harri Deutsch, 1997
  • C. W. Misner, K. S. Thorne, J. A. Wheeler, “Gravitation”, Princeton University Press, 2017
  • U. E. Schröder, “Gravitation – Einführung in die Allgemeine Relativitätstheorie”, Harri Deutsch, 2011
  • N. Straumann, “General Relativity”, Springer, 2012
  • R. Wald, "General Relativity", University of Chicago Press, 1984
  • S. Weinberg, “Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity”, Wiley, 1972
  • A. Zee, “Einstein Gravity in a Nutshell”, Princeton University Press, 2013

Requirements for Course Achievement / Academic Record

  • Course Achievement ("Studienleistung"):
    Active and regular participation in the tutorials, including solutions to 50% of the homework problems.
  • Academic Record ("Prüfungsleistung"):
    Oral or written exam.

Further details will be given in the lecture/tutorials.

Lecture notes

See ILIAS page.

Exercise sheets

See ILIAS page.
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