The General Theory of Relativity - A Mathematical Exposition

The General Theory of Relativity: A Mathematical Exposition will serve readers as a modern mathematical introduction to the general theory of relativity. Throughout the book, examples, worked-out problems, and exercises (with hints and solutions) are furnished. Topics in this book include, but are not limited to:

tensor analysis
the special theory of relativity
the general theory of relativity and Einstein's field equations
spherically symmetric solutions and experimental confirmations
static and stationary space-time domains
black holes
cosmological models
algebraic classifications and the Newman-Penrose equations
the coupled Einstein-Maxwell-Klein-Gordon equations
appendices covering mathematical supplements and special topics
Mathematical rigor, yet very clear presentation of the topics make this book a unique text for both university students and research scholars.

Anadijiban Das has taught courses on Relativity Theory at The University College of Dublin, Ireland, Jadavpur University, India, Carnegie-Mellon University, USA, and Simon Fraser University, Canada. His major areas of research include, among diverse topics, the mathematical aspects of general relativity theory.

Andrew DeBenedictis has taught courses in Theoretical Physics at Simon Fraser University, Canada, and is also a member of The Pacific Institute for the Mathematical Sciences. His research interests include quantum gravity, classical gravity, and semi-classical gravity.

List of contents

Tensor Analysis on Differentiable Manifolds.- The Pseudo-Riemannian Space-Time Manifold M4.- Spherically Symmetric Space-Time Domains.- Static and Stationary Space-Time Domains.- Black Holes.- Cosmology.- Algebraic Classification of Field Equations.- The Coupled Einstein-Maxwell-Klein-Gordon Equations.- Appendix 1: Variational Derivation of Differential Equations.- Appendix 2: Partial Differential Equations.- Appendix 3: Canonical Forms of Matrices.- Appendix 4: Conformally Flat Space-Times and "the Fifth Force".- Appendix 5: Linearized Theory and Gravitational Waves.- Appendix 6: Exotic Solutions: Wormholes, Warp-Drives, and Time Machines.- Appendix 7: Gravitational Instantons.- Appendix 8: Computational Symbolic Algebra Calculations.- References.- Index of Symbols.- Index.

About the author

Anadijiban Das, Simon Fraser University, Burnaby, British Columbia, Canada, [e-mail] 

Andrew DeBenedictis, Simon Fraser University, Burnaby, British Columbia, Canada, [e-mail]

Summary

The General Theory of Relativity: A Mathematical Exposition will serve readers as a modern mathematical introduction to the general theory of relativity. Throughout the book, examples, worked-out problems, and exercises (with hints and solutions) are furnished. Topics in this book include, but are not limited to: 

tensor analysis 
the special theory of relativity 
the general theory of relativity and Einstein’s field equations 
spherically symmetric solutions and experimental confirmations 
static and stationary space-time domains 
black holes 
cosmological models 
algebraic classifications and the Newman-Penrose equations 
the coupled Einstein-Maxwell-Klein-Gordon equations 
appendices covering mathematical supplements and special topics
Mathematical rigor, yet very clear presentation of the topics make this book a unique text for both university students and research scholars.

Anadijiban Das has taught courses on Relativity Theory at The University College of Dublin, Ireland, Jadavpur University, India, Carnegie-Mellon University, USA, and Simon Fraser University, Canada. His major areas of research include, among diverse topics, the mathematical aspects of general relativity theory.

Andrew DeBenedictis has taught courses in Theoretical Physics at Simon Fraser University, Canada, and is also a member of The Pacific Institute for the Mathematical Sciences. His research interests include quantum gravity, classical gravity, and semi-classical gravity.

Additional text

From the reviews:
“The book under review grew out of courses that were taught by the senior author (Das) over the years … . it does serve as a useful reference work for researchers who would prefer a direct exposition of the topics that they are involved with.” (David H. Delphenich, Mathematical Reviews, May, 2013)
“This advanced work is only for those who are familiar with high-level tensor mathematics or who specialize in gravitation theory. … The authors provide detailed proofs to theorems with elaborate discussion. … Every chapter contains exercises with hints to solve them or complete solutions. An exhaustive list of references and a good index support the text. Summing Up: Recommended. Graduate students, researchers/faculty, and professionals.” (N. Sadanand, Choice, Vol. 50 (5), January, 2013)
“The General Theory of Relativity: A Mathematical Exposition is … written in a very clear style and the mathematics is done carefully and in detail. There are also a lot of ‘examples, worked-out problems, and exercises (with hints and solutions),’ … so it is certainly a pedagogically sound enterprise well worth the price of admission. I am happy to be able to recommend it.” (Michael Berg, The Mathematical Association of America, August, 2012)

Report

From the reviews:
"The book under review grew out of courses that were taught by the senior author (Das) over the years ... . it does serve as a useful reference work for researchers who would prefer a direct exposition of the topics that they are involved with." (David H. Delphenich, Mathematical Reviews, May, 2013)
"This advanced work is only for those who are familiar with high-level tensor mathematics or who specialize in gravitation theory. ... The authors provide detailed proofs to theorems with elaborate discussion. ... Every chapter contains exercises with hints to solve them or complete solutions. An exhaustive list of references and a good index support the text. Summing Up: Recommended. Graduate students, researchers/faculty, and professionals." (N. Sadanand, Choice, Vol. 50 (5), January, 2013)
"The General Theory of Relativity: A Mathematical Exposition is ... written in a very clear style and the mathematics is done carefully and in detail. There are also a lot of 'examples, worked-out problems, and exercises (with hints and solutions),' ... so it is certainly a pedagogically sound enterprise well worth the price of admission. I am happy to be able to recommend it." (Michael Berg, The Mathematical Association of America, August, 2012)

Product details

• Authors: Anadijiba Das, Anadijiban Das, Andrew Debenedictis
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 01.01.2014
• EAN: 9781489987174
• ISBN: 978-1-4899-8717-4
• No. of pages: 678
• Dimensions: 164 mm x 35 mm x 235 mm
• Weight: 1048 g
• Illustrations: XXVI, 678 p.
• Subjects: Natural sciences, medicine, IT, technology > Physics, astronomy > Theoretical physics; Gravitation, C, Applications of Mathematics, Cosmology, Physics and Astronomy, Relativity physics, Mathematical physics, Numerical analysis, Manifolds (Mathematics), Mathematical modelling, Mathematical Applications in the Physical Sciences, Global analysis (Mathematics), Global Analysis and Analysis on Manifolds, Classical and Quantum Gravity, Classical and Quantum Gravitation, Relativity Theory