- Provides a comprehensive and detailed introduction to general relativity
- Discusses exciting topics in an understandable way, from Newton's theory of gravity to the metrics of rotating black holes
- Motivates with interspersed exercises and problems
This book offers physics students a clear introduction to general relativity: What is the energy-momentum tensor and what do the Friedmann equations describe? How can space-time be modelled using a manifold? What is the Schwarzschild solution and when are Kruskal coordinates needed? Can energy be extracted from the ergosphere of a rotating black hole? These questions and many more are answered in this book. The didactic focus is on simple and understandable communication and detailed presentation of the complex topic. The book deliberately avoids phrases such as "it can be shown that..." or "as can be easily shown, it holds" and explains the calculation steps in exercises and derivations in detail.
For review purposes, the essential points from Lagrange mechanics, electrodynamics and special relativity theory are briefly presented. Readers should have prior knowledge of mathematics, particularly in the areas of linear algebra and complex numbers. Necessary advanced mathematics, such as differential geometry, is introduced carefully, appropriately and comprehensively. Concrete problems with complete, detailed solutions encourage readers to think and calculate along with the author.
The book is divided into five parts:
- Fundamentals of special relativity theory and consequences for relativistic mechanics and electrodynamics
- Important results of Newton's model of gravitation and the need for a new theory of gravitation, modelling of space-time using a Lorentz manifold
- Physical focus: heuristic and formal derivation of Einstein's equations
- Astrophysical objects: derivation of the Schwarzschild metric, the interior of a star, non-rotating, rotating and charged black holes, Eddington-Finkelstein and Kruskal coordinates, Penrose diagrams
- Application to our universe: homogeneity and isotropy of the universe, Robertson-Walker metric, Friedmann equations
The author Michael Ruhrländer studied mathematics at the University of Essen and obtained his doctorate in Wuppertal. He has been a lecturer in mathematics and statistics at the Technical University of Applied Sciences in Bingen since 2010.
