General Relativity

1 Physics in External Gravitational Fields.- 2 Einstein's Field Equations.- 3 The Schwarzschild Solution and Classical Tests of General Relativity.- 4 Weak Gravitational Fields.- 5 The Post-Newtonian Approximation.- 6 White Dwarfs and Neutron Stars.- 7 Black Holes.- 8 The Positive Mass Theorem.- 9 Differentiable Manifolds.- 10 Tangent Vectors, Vector and Tensor Fields.- 11 The Lie Derivative.- 12 Differential Forms.- 13 Affine Connections.- 14 Some Details.- A Fundamental Equations for Hypersurfaces.- B Ricci Curvature of Warped Products.- C Frobenius Integrability Theorem.- D Collection of Important Formulas.- References.

From the reviews:

"In this book Norbert Straumann presents a pedagogically precise and highly informative account of both the physical and advanced mathematical concepts that a professional working in this field requires. The essential differential geometry background is placed in an extensive part ... . the treatment is both physically rigorous and comprehensive. This book is an important acquisition for anyone working in this area." (Geoffrey Bicknell, Australian Physics, Vol. 42 (4), September/October, 2005)

"This text provides a comprehensive and timely introduction to general relativity. ... The book addresses undergraduate and graduate students in physics, astrophysics and mathematics. It is very well structured and should become a standard text for a modern treatment of gravitational physics. The clear presentation of differential geometry makes it also useful for strong theory and other fields of physics, classical as well as quantum." (ETDE Energy Database Energiedatenbank, November, 2004)

"From the earliest sections, Straumann makes absolutely no pretence that this is a beginner's guide to general relativity ... . There are points of interest for those disinclined (or unable) to follow the maths in detail. ... this book is primarily aimed at those who want to get very, very intimate with the mathematics of general relativity in an astrophysical .... context and who are endowed with a considerable background in all three subjects. ... this may be the ultimate specialist textbook." (Roger Feasey, Journal of the Auckland Astronomical Society, 2005)