General Relativity
A Geometric Approach

A clear and concise introduction to the theory of general relativity for final-year undergraduate mathematics or physics students.

Malcolm Ludvigsen (Author)

9780521630191, Cambridge University Press

Hardback, published 28 May 1999

230 pages, 55 b/w illus. 94 exercises
26.2 x 18.3 x 2 cm, 0.655 kg

'… 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

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 and concise 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. 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. 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 are illustrated with worked examples. Solutions and hints to selected problems are provided at the end of the book. This textbook will enable the student to develop a sound understanding of the theory of general relativity.

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.

Subject Areas: Physics [PH], Applied mathematics [PBW]