General Relativity

A Geometric Approach

Malcolm Ludvigsen (Linköpings Universitet, Sweden)

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English

Cambridge University Press
04 October 1999

Applied mathematics; Relativity physics

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.

By: Malcolm Ludvigsen (Linköpings Universitet Sweden)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 262mm, Width: 183mm, Spine: 20mm
Weight: 655g
ISBN: 9780521630191
ISBN 10: 0521630193
Pages: 230
Publication Date: 04 October 1999
Audience: College/higher education , Professional and scholarly , Primary , Undergraduate
Format: Hardback
Publisher's Status: Active

Part I. The Concept of Spacetime: 1. Introduction; 2. Events; Part II. Flat Spacetime and Special Relativity: 3. Flat spacetime; 4. The geometry of flat spacetime; 5. Energy; 6. Tensors; 7. Tensor fields; 8. Field equations; Part III. Curved Spacetime and Gravity: 9. Curved spacetime; 10. Curvature and gravity; 11. Null congruences; 12. Asymptotic flatness and symmetries; 13. Schwarzschild; 14. Black holes and singularities; Part IV. Cosmology: 15. The spacetime of the universe; 16. Relativistic cosmology; Solutions and hints to selected exercises; Bibliography; Index.

Reviews for General Relativity: A Geometric Approach

' ... written for final-year undergraduates mathematics or physics students ... This short, elegant book describes the major ideas of special and general relativity with unprecedented clarity and mathematical depth.' Physics Today '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, Max Planck Institute for Gravitational Physics, Potsdam 'The author has done a good work. The book is pedagogic and reads easily ... this book is recommended for undergraduate studies both in physics and in mathematics and also for faculty libraries ...'. A. F. Ranada, European Journal of Physics '... the book introduces many refreshing novelties to the subject ... Malcolm Ludvigsen's book is never dull and this is a major thing in its favour'. Graham S. Hall, General Relativity and Gravitation