General Relativity and Cosmology

Module PH2043

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Basic Information

PH2043 is a semester module in English language at Master’s level which is offered in winter semester.

This Module is included in the following catalogues within the study programs in physics.

  • General catalogue of special courses
  • Specific catalogue of special courses for nuclear, particle, and astrophysics

If not stated otherwise for export to a non-physics program the student workload is given in the following table.

Total workloadContact hoursCredits (ECTS)
300 h 110 h 10 CP

Responsible coordinator of the module PH2043 is Alejandro Ibarra.

Content, Learning Outcome and Preconditions


  1. Introduction to differential geometry.
  2. The equivalence principle. Gravitation. The Einstein’s equation. Newtonian limit.
  3. The Schwartzschild Metric. Black holes.
  4. The weak field approximation. Gravitational waves.
  5. Cosmology: Homogeneity and isotropy, Robertson-Walker metric.
  6. Friedmann Equation. Hubble parameter. The expanding Universe.

Learning Outcome

After participation in the Module the student is able to:

  1. Understand the origin of gravity as the effect of the curvature of spacetime.
  2. Describe the classical experimental tests of general relativity: the deflection of light, the precession of perihelia and gravitational redshift.
  3. Understand the basic physics of black holes.
  4. Understand the basic properties of gravitational waves.
  5. Describe the different stages of the expanding Universe and derive the Hubble’s law.


No prior knowledge necessary, beyond the admission requirements for the master's degree.

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

VU 6 General Relativity and Cosmology Ibarra, A.
Mitwirkende: Ingenhütt, S.Rappelt, A.
Montag, 12:00–14:00
Dienstag, 08:00–10:00
sowie Termine in Gruppen

Learning and Teaching Methods

Lecture, beamer presentation, board work, exercises in individual and group work


practise sheets


  • Spacetime and Geometry, S.Carroll
  • Cosmology, S. Weinberg.
  • The Early Universe, E. Kolb, S. Turner

Module Exam

Description of exams and course work

In a written exam the learning outcome is tested using comprehension questions and sample problems.

In accordance with §12 (8) APSO the exam can be done as an oral exam. In this case the time duration is 40 minutes.

Exam Repetition

There is a possibility to take the exam at the end of the semester.

Current exam dates

Currently TUMonline lists the following exam dates. In addition to the general information above please refer to the current information given during the course.

Prüfung zu Allgemeine Relativitätstheorie und Kosmologie
Mi, 15.2.2017, 10:30 bis 12:30 Physik I: 2502
bis 15.1.2017 (Abmeldung bis 8.2.2017)
Do, 13.4.2017, 11:00 bis 13:00 Physik I: 2503
bis 3.4.2017 (Abmeldung bis 6.4.2017)

Condensed Matter

When atoms interact things can get interesting. Fundamental research on the underlying properties of materials and nanostructures and exploration of the potential they provide for applications.

Nuclei, Particles, Astrophysics

A journey of discovery to understanding our world at the subatomic scale, from the nuclei inside atoms down to the most elementary building blocks of matter. Are you ready for the adventure?


Biological systems, from proteins to living cells and organisms, obey physical principles. Our research groups in biophysics shape one of Germany's largest scientific clusters in this area.