General Relativity: A Geometric Approach

Starting with the idea of an event and finishing with a description of the standard big-bang model of the Universe, this textbook provides a clear, concise and up-to-date introduction to the theory of general relativity, suitable for final-year undergraduate mathematics or physics students. Throughout, the emphasis is on the geometric structure of spacetime, rather than the traditional coordinate-dependent approach. This allows the theory to be pared down and presented in its simplest and most elegant form. Topics covered include flat spacetime (special relativity), Maxwell fields, the energy-momentum tensor, spacetime curvature and gravity, Schwarzschild and Kerr spacetimes, black holes and singularities, and cosmology. In developing the theory, all physical assumptions are clearly spelled out and the necessary mathematics is developed along with the physics. Exercises are provided at the end of each chapter and key ideas in the text are illustrated with worked examples. Solutions and hints to selected problems are also provided at the end of the book. This textbook will enable the student to develop a sound understanding of the theory of general relativity, and all the necessary mathematical machinery.

"This short, elegant book describes the major ideas of special and general relativity with unprecedented clarity and mathematical depth.... Ludvigsen's book is a very good addition to the library of anyone who is interested in general relativity, black holes, and cosmology. Many who learned or studied general relativity from other sources would gain from the depth and beauty of the geometrical approach so beautifully described here." Physics Today

"A valuable effort has been made towards keeping mathematical language and machinery as simple as possible, always introducing the mathematical tools required at each step. On the other hand, all physical assumptions are clearly spelled out and their translation into mathematics is carefully made..." Mathematical Reviews

"Ludvigsen's book provides us with an elegant modern introduction to Einstein's general relativity; it is comprehensive, brief and very readable." Professor Sir Roger Penrose, Mathematical Institute, University of Oxford

"...a clear, clean, concise introduction to mathematical general relativity. It is a pleasure to see so many important topics discussed with such economy and care." Professor Bernard F. Schutz, Albert Einstein Institute, Max Planck Institute for Gravitational Physics, Potsdam

"Ludvigsen's textbook is almost unique in its emphasis on the geometrical foundations of the theory...a refreshing and intriguing review of the subject." Dr. John Stewart, Department of Applied Mathematics and Theoretical Physics, University of Cambridge

"...a simple and elegant introduction to the subject...written in a pleasant style, with some humor, which makes it quite readable for the properly prepared student...a welcome addition to the literature." American Journal of Physics