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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.

Module version of SS 2011

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.

available module versions
WS 2022/3WS 2021/2WS 2020/1WS 2019/20WS 2018/9WS 2017/8SS 2011

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.

  • Specific catalogue of special courses for nuclear, particle, and astrophysics
  • Complementary catalogue of special courses for condensed matter physics
  • Complementary catalogue of special courses for Biophysics
  • Complementary catalogue of special courses for Applied and Engineering Physics
  • Specialization Modules in Elite-Master Program Theoretical and Mathematical Physics (TMP)

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 in the version of SS 2011 was 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

VO 4 General Relativity and Cosmology Ibarra, A. Mon, 08:00–10:00, PH HS2
Wed, 10:00–12:00, PH HS2
UE 2 Exercise to General Relativity and Cosmology
Responsible/Coordination: Ibarra, A.
dates in groups

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

The exam may be repeated 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.

Exam to General Relativity and Cosmology
Thu, 2024-02-15, 11:00 till 14:00 2501
till 2024-01-15 (cancelation of registration till 2024-02-08)
Mon, 2024-03-25, 11:00 till 14:00 2502
till 2024-03-21
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