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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 WS 2018/9

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 or German 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 90 h 10 CP

Responsible coordinator of the module PH2043 in the version of WS 2018/9 was Martin Beneke.

Content, Learning Outcome and Preconditions


  1. Introduction to the concepts of relativity and covariance
  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.
  7. The Early 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.
  6. Uniderstand particle physics in the early, hot Universe


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 Beneke, M. Mon, 08:00–10:00, PH HS2
Wed, 10:00–12:00, PH HS2
and singular or moved dates
UE 2 Exercise to General Relativity and Cosmology König, M.
Responsible/Coordination: Beneke, M.
dates in groups

Learning and Teaching Methods

This module consists of a lecture and an exercise course.

The lecture is designed for the presentation of the subject, usually by blackboard presentation. The focus resides on theoretical foundations of the field, presentation of methods and simple, illustrative examples. Command of basic methods is deepened and practised through homework problems, which cover important aspects of the field.

In the exercise course the learning content is deepened and exercised using problem examples, developing the analytic skills of the students and their ability to perform calculations. The homework problems are discussed in the exercise by the students themselves under the supervision of a tutor in order to develop the skills to explain a physics problem logically.


Lecture, blackboard, problem sets, presentation, homework problems and their discussion in tutorial groups, web page


  • S. Caroll: Spacetime and Geometry, Pearson, (2013)
  • S. Weinberg: Gravitation and Cosmology, Wiley, (1972)
  • E.W. Kolb & M.S. Turner: The Early Universe, Westview Press, (1994)

Module Exam

Description of exams and course work

There will be a written exam of 180 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using calculation problems and comprehension questions.

For example an assignment in the exam might be:

  • Calculate the motion of a test particle in curved space-time.
  • Derive some of the most important known solutions to the Einstein field equations.
  • Compute the emission of gravitational waves of a given source.

Participation in the tutorials is strongly recommended since the exercises prepare for the problems of the exam and rehearse the specific competencies.

There will be a bonus (one intermediate stepping of "0,3" to the better grade) on passed module exams (4,3 is not upgraded to 4,0). The bonus is applicable to the exam period directly following the lecture period (not to the exam repetition) and subject to the condition that the student passes the mid-term. The latter is considered passed if 50% of the points in the homework problems have been achieved.

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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