| Univ. Bremen Prof. E. Hackmann | Introduction to General Relativity (S2, compulsory, 9 ECTS) |
| Learning Outcomes: | Participants do understand the principles underlying General Relativity and are able to do basic calculations in General Relativity. |
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| Prerequisites | Basic courses in Physics on mechanics, electrodynamics, quantum mechanics. |
| Program | First, a short repetition of Special Relativity is given. The introduction to General Relativity starts with mathematical preliminaries, that is, the differentiable manifold, coordinates and coordinate transformations, the Lie-derivative, the covariant derivative and the curvature tensor, and finally the space-time metric. Next the geodesic equation as equation of motion for freely falling point-like particles and for light rays is introduced and discussed in terms of a post-Newtonian approximation. Then the gravitational field equation, the Einstein equation, is introduced. Simple solutions of that equation like the Schwarzschild or Reissner-Nordström solutions are derived. These solutions are interpreted in terms of the influence on light rays and particles. In particular, the horizon and the singularity will be defined. Also the post-Newtonian approximation is discussed and the Perihelion shift is derived. With a weak field approximation of the metric gravitational waves and their sources are derived from the Einstein equations. The principles of their detection is also explained. An outlook towards the Kerr solution is given. Finally, a short introduction to cosmology is given and the Friedman equations are derived and solved. |
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| Adopted Textbooks | A list of references will be provided at the start of the semester. |
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