General Relativity and Cosmology

1. Review of Special Relativity
2. Manifolds.
3. The Equivalence Principle and Spacetime Curvature.
4. Gravitation.
5. The Schwarzschild Geometry and Black Holes.
6. Gravitational radiation.
7. Cosmology.

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.

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 http://users.ph.tum.de/ga49yar/19ws-art/

• 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)

There will be a written exam of 90 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 trajectories of light or massive objects around a star
• Determine the evolution of a Universe with a certain energy content.

In the exam no learning aids are permitted.

Participation in the exercise classes 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 of passing the voluntary test exam during the semester