General Relativity. A Geometric Approach

"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 E 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 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.