# Spacetime, Geometry and Gravitation

• Pankaj Sharan
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
5. Back Matter
Pages 351-355

### 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

• Pankaj Sharan
• 1
1. 1.Physics DepartmentJamia Millia IslamiaNew DelhiIndia

### Bibliographic information

• 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
• Print ISBN 978-3-7643-9970-2
• Online ISBN 978-3-7643-9971-9
• Series Print ISSN 1544-9998
• Series Online ISSN 2197-1846
• Buy this book on publisher's site