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 of theoretical astrophysics at Heidelberg University since 2003. He studied physics and astronomy at Munich University and obtained his PhD in 1992, for which he received the Otto Hahn Medal of the Max Planck Society. He was a post-doc at the Max Planck Institute for Astrophysics in Garching and at the Harvard-Smithsonian Center for Astrophysics. He received the Ludwig Biermann Prize of the German Astronomical Society in 1996 and became a lecturer in astronomy at Munich University in 1998. Between 1998 and 2003, he built up and led the German scientific contribution to the Planck satellite mission. He acted as the dean of the department of physics and astronomy at Heidelberg University from 2006-08. Matthias Bartelmann's research interests are centered on structure formation in the Universe, in particular the study of the dark-matter distribution by means of gravitational lensing and probes of non-linear evolution, the problem of dark energy and the physics of the cosmic microwave background.
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