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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.

Black holes (Astronomy) --- General relativity (Physics) --- Mathematical physics --- 524.88 --- 524.88 Special hypotheses. Black holes. Antimatter --- Special hypotheses. Black holes. Antimatter --- Physical mathematics --- Physics --- Relativistic theory of gravitation --- Relativity theory, General --- Gravitation --- Relativity (Physics) --- Frozen stars --- Compact objects (Astronomy) --- Gravitational collapse --- Stars --- Mathematics --- Mathematical physics. --- Mathematics. --- General relativity (Physics).