This book provides an introduction to the mathematics and physics of general relativity, its basic physical concepts, its observational implications, and the new insights obtained into the nature of space-time and the structure of the universe. It introduces some of the most striking aspects of Einstein's theory of gravitation: black holes, gravitational waves, stellar models, and cosmology. It contains a self-contained introduction to tensor calculus and Riemannian geometry, using in parallel the language of modern differential geometry and the coordinate notation, more familiar to physicists. The author has strived to achieve mathematical rigour, with all notions given careful mathematical meaning, while trying to maintain the formalism to the minimum fit-for-purpose. Familiarity with special relativity is assumed.

The overall aim is to convey some of the main physical and geometrical properties of Einstein's theory of gravitation, providing a solid entry point to further studies of the mathematics and physics of Einstein equations.

Concise modern introduction to the mathematical tools Precise mathematical treatment of all problems addressed Can be used for an introductory course on a mathematically-minded introduction to Einstein's theory of gravitation

Autorentext
Piotr T. Chrüciel is Professor of Gravitational Physics at the Faculty of Physics of the University of Vienna, where he heads the gravitational physics group. His previous academic postings include the University of Oxford, where he was a lecturer with title of Professor at the Mathematical Institute and a Fellow of Hertford College. He is a Life Member of Clare Hall, Cambridge. He is a specialist in all aspects of mathematical general relativity.

Inhalt
Introduction to tensor calculus and Riemannian geometry.- Curved space-time.- The Schwarzschild metric.- Weak fields, gravitational waves.- Stars.- Cosmology.