Black holes present one of the most fascinating predictions of Einstein's general theory of relativity. There is strong evidence of their existence through observation of active galactic nuclei, including the centre of our galaxy, observations of gravitational waves, and others.

There exists a large scientific literature on black holes, including many excellent textbooks at various levels. However, most of these steer clear from the mathematical niceties needed to make the theory of black holes a mathematical theory. Those which maintain a high mathematical standard are either focused on specific topics, or skip many details. The objective of this book is to fill this gap and present a detailed, mathematically oriented, extended introduction to the subject.

The book provides a wide background to the current research on all mathematical aspects of the geometry of black hole spacetimes.

Table of Contents

Part I: Global Lorentzian geometry

1 Basic notions

2 Elements of causality

3 Some applications

Part II: Black holes

4 An introduction to black holes

5 Further selected solutions

6 Extensions, conformal diagrams

7 Projection diagrams

8 Dynamical black holes

Appendices

A The Lie derivative

B Covariant derivatives

C Curvature

D Exterior algebra

E Null hyperplanes

F The geometry of null hypersurfaces

G The general relativistic Cauchy problem

H A collection of identities

About the Author

Univ. Prof. Dr. Piotr T. Chrusciel is Professor of Gravitational Physics and Head of the Gravitational Physics Group, Faculty of Physics, University of Vienna, Austria.