Introduction to General Relativity (WS24/25)

Lecturer

Prof. Dr. Stefan Dittmaier and Dr. Maximilian Stahlhofen

Dates

• Lecture: 4 hours, Mon 10-12 (Seminaraum I), Tue 14-16 (Hörsaal I), start: 14.10.2024

• Tutorial: 2 hours, Fri 14-16 (Seminarraum I)

ILIAS link

Content

• 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

Prerequisites

Theoretical Mechanics, Electrodynamics, and Special Relativity

Literature

• 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

Exercise sheets