The General Theory of Relativity
A Mathematical Approach

Discusses the general theory of relativity, Lie derivatives, rotating black holes, with a focus on basics of cosmology and astrophysics.

Farook Rahaman (Author)

9781108837996, Cambridge University Press

Hardback, published 30 September 2021

422 pages
24.7 x 18.7 x 2.5 cm, 0.83 kg

The book aims to expound the general theory of relativity with a mathematical point of view. Catering to the needs of postgraduate students and researchers in the field of astrophysics and mathematical physics, it offers the readers a comprehensive understanding of the advanced topics of the subject matter. It specifically discusses the mathematical foundation of tensor calculus, gives a background of geodesics, Einstein's field equations, linearised gravity, spacetime of spherically symmetric distribution of matter and black holes, and particle and photon orbits in spacetime. Apart from the formulation of general relativity, Lie derivatives and its applications, and causality of spacetime are also discussed in detail. Certain preliminary concepts of extrinsic curvature, Lagrangian formalism of general theory of relativity and 3 + 1 decomposition of space-time are covered and are provided in the book as appendices.

Preface
Acknowledgement
1. Tensor calculus – a brief overview
2. Geodesics
3. Einstein field equations
4. Linearized gravity
5. Lie derivatives and Killing's equation
6. Spacetimes of spherically symmetric distribution of matter and black holes
7. Particle and photon orbits in the Schwarzschild spacetime
8. Causal structure of spacetime
9. Exact solutions of Einstein equations and their causal structures
10. Rotating Black holes
11. Elementary cosmology
12. Elementary astrophysics
Appendix A. Extrinsic curvature
Appendix B. Lagrangian formalism of general relativity
Appendix C. 3+1 decomposition
Bibliography
Index.

Subject Areas: Astrophysics [PHVB], Applied physics [PHV], Mathematical physics [PHU], Relativity physics [PHR], Physics [PH], Mathematics & science [P]