# Spacetime, Geometry and Gravitation

## Benefits

• Physically intuitive, but mathematically rigorous writing style

• Early introduction to geometric quantities allows students to learn simpler topics in general relativity (Newtonian limit, Schwarzschild solution, bending of light in a gravitational field, ...)

• Approved in lectures given by the author for several years

• Provides many exercises and answers

Textbook

Part of the Progress in Mathematical Physics book series (PMP, volume 56)

1. Front Matter
Pages i-xiv
2. ### Spacetime

1. Front Matter
Pages 1-1
2. Pages 3-38
3. Pages 39-53
4. Pages 55-63
5. Pages 65-80
3. ### Geometry

1. Front Matter
Pages 81-81
2. Pages 83-96
3. Pages 97-113
4. Pages 115-132
5. Pages 133-153
6. Pages 155-179
7. Pages 181-207
4. ### Gravitation

1. Front Matter
Pages 209-209
2. Pages 211-235
3. Pages 237-256
4. Pages 257-286
5. Pages 287-315
6. Pages 317-327
7. Pages 329-350

### Introduction

This is an introductory book on the general theory of relativity based partly on lectures given to students of M.Sc. Physics at my university. The book is divided into three parts. The ?rst part is a preliminary course on general relativity with minimum preparation. The second part builds the ma- ematical background and the third part deals with topics where mathematics developed in the second part is needed. The ?rst chapter gives a general background and introduction. This is f- lowed by an introduction to curvature through Gauss’ Theorema Egregium. This theorem expresses the curvature of a two-dimensional surface in terms of intrinsic quantitiesrelatedtothein?nitesimaldistancefunctiononthesurface.Thestudent isintroducedtothemetrictensor,Christo?elsymbolsandRiemanncurvaturet- sor by elementary methods in the familiar and visualizable case of two dimensions. This early introduction to geometric quantities equips a student to learn simpler topics in general relativity like the Newtonian limit, red shift, the Schwarzschild solution, precession of the perihelion and bending of light in a gravitational ?eld. Part II (chapters 5 to 10) is an introduction to Riemannian geometry as - quired by general relativity. This is done from the beginning, starting with vectors and tensors. I believe that students of physics grasp physical concepts better if they are not shaky about the mathematics involved.

### Keywords

Christoffel symbol Friedman equation Gravity Kerr solution Relativity Riemannian geometry Schwarzschild solution Theorema Egregium general relativity general theory of relativity gravitation gravitational wave spacetime weak gravitational field

#### Authors and affiliations

1. 1.Physics DepartmentJamia Millia IslamiaNew DelhiIndia

### Bibliographic information

• Book Title Spacetime, Geometry and Gravitation
• Authors Pankaj Sharan
• Series Title Progress in Mathematical Physics
• DOI https://doi.org/10.1007/978-3-7643-9971-9
• Copyright Information Birkhäuser Basel 2009
• Publisher Name Birkhäuser Basel
• eBook Packages Physics and Astronomy Physics and Astronomy (R0)
• Hardcover ISBN 978-3-7643-9970-2
• eBook ISBN 978-3-7643-9971-9
• Series ISSN 1544-9998
• Series E-ISSN 2197-1846
• Edition Number 1
• Number of Pages XIV, 355
• Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
• Additional Information Jointly published with Hindustan Book Agency, India
• Topics
• Buy this book on publisher's site

## Reviews

From the reviews:

“The book is structured into three parts. The first part … offers preliminary topics on general relativity. … The second part is a comprehensive and accurate incursion in the mathematical background of relativity theory. … The last part, entitled Gravitation, contains six chapters dealing with the Einstein equation … cosmology and special topics. Interesting exercises with complete answers simplify the understanding of the presented material. The textbook is recommended to advanced graduates and researchers.” (Ferenc Szenkovits, Studia Universitatis Babes-Bolyai, Mathematica, Vol. LV (4), December, 2010)

“This book provides the reader with a very gentle introduction to the main ideas and concepts of general relativity. This work is particularly suitable for students who are interested in general relativity or are beginning to study this subject. Moreover, the author presents the reader with a number of problems and provides worked-out solutions, which will surely help the reader to obtain a deeper of interest to students who seek a smooth introduction to general relativity.” (Guglielmo Fucci, Mathematical Reviews, Issue 2011 m)

"This book meets my teaching needs, as it presents a very solid foundation for students who seek a comprehensive introduction into the difficult field of the general theory of relativity. The mathematical background is treated in a rigorous and nevertheless understandable style. Those readers who are novices in the field will welcome the fact that the author provides an abundance of carefully selected exercises together with their solutions. In summary, I will recommend this valuable textbook to my students and use it as the main text for my lectures." - Prof. Dr. P. Wirtz, Faculty of Computer Science and Mathematics, Hochschule Hegensburg, Germany