General Relativity
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Bartelmann, Matthias: General Relativity, Heidelberg: Heidelberg University Publishing, 2019.

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ISBN 978-3-947732-60-9 (Softcover)
ISBN 978-3-947732-59-3 (PDF)

Published 10.10.2019.


Matthias Bartelmann

General Relativity

Lecture Notes

Einstein‘s theory of general relativity is still the valid theory of gravity and has been confirmed by numerous tests and measurements. It is built upon simple principles and relates the geometry of space-time to its matter-energy content. These lecture notes begin by introducing the physical principles and by preparing the necessary mathematical tools taken from differential geometry. Beginning with Einstein’s field equations, which are introduced in two different ways in the lecture, the motion of test particles in a gravitational field is then discussed, and it is shown how the properties of weak gravitational fields follow from the field equations. Solutions for compact objects and black holes are derived and discussed as well as cosmological models. Two applications of general relativity to astrophysics conclude the lecture notes.

Matthias Bartelmann is professor for theoretical astrophysics at Heidelberg University. He mostly addresses cosmological questions, concerning in particular the formation and evolution of cosmic structures.

Instead of a preface
1 Introduction
2 Differential Geometry I
3 Differential Geometry II
4 Physics in Gravitational Fields
5 Differential Geometry III
6 Einstein’s Field Equations
7 Weak Gravitational Fields
8 The Schwarzschild Solution
9 The Schwarzschild Spacetime
10 Schwarzschild Black Holes
11 Charged, Rotating Black Holes
12 Homogeneous, Isotropic Cosmology
13 Relativistic Astrophysics
Appendix A Electrodynamics
Appendix B Differential Geometry
Appendix C Penrose-Carter diagrams