This 2004 textbook fills a gap in the literature on general relativity by providing the advanced student with practical tools for the computation of many physically interesting quantities. The context is provided by the mathematical theory of black holes, one of the most elegant, successful, and relevant applications of general relativity. Among the topics discussed are congruencies of timelike and null geodesics, the embedding of spacelike, timelike and null hypersurfaces in spacetime, and the Lagrangian and Hamiltonian formulations of general relativity. Although the book is self-contained, it is not meant to serve as an introduction to general relativity. Instead, it is meant to help the reader acquire advanced skills and become a competent researcher in relativity and gravitational physics. The primary readership consists of graduate students in gravitational physics. It will also be a useful reference for more seasoned researchers working in this field.

• Short, concise and to the point • Focuses on practical methods of computation in general relativity • Provides advanced skills for those beginning research in this field

### Contents

Preface; Notation and conventions; 1. Fundamentals; 2. Geodesic congruences; 3. Hypersurfaces; 4. Lagrangian and Hamiltonian formulation of general relativity; 5. Black holes; References; Index.

### Reviews

'… an elegant, thoughtful, useful and altogether commendable publication.' Contemporary Physics

'The author puts emphasis on training the readers and equipping them with the relevant skills of a working relativist. The text reaches a high pedagogical standard … In this way the author succeeds in closing a gap in the existing text book literature especially for a readership mainly oriented towards physics.' Monatshefte für Mathematik