Problem Book in Relativity and Gravitation

Alan P. Lightman is professor of the practice of the humanities at the Massachusetts Institute of Technology. His books include Screening Room and Einstein's Dreams. William H. Press is the Warren J. and Viola M. Raymer Professor in Computer Science and in Integrative Biology at the University of Texas, Austin. Richard H. Price is senior lecturer in physics at the Massachusetts Institute of Technology. He is the coeditor of Black Holes. Saul A. Teukolsky is the Hans A. Bethe Professor of Physics and Astrophysics at Cornell University and the coauthor of Black Holes, White Dwarfs and Neutron Stars. Press and Teukolsky are coauthors in the Numerical Recipes book series.

PREFACE vii

NOTATION xi

PROBLEMS SOLUTIONS

1 Special-Relativistic Kinematics 3 133

2 Special-Relativistic Dynamics 11 159

3 Special-Relativistic Coordinate Transformations, Invariants and Tensors 15 173

4 Electromagnetism 23 192

5 Matter and Radiation 28 205

6 Metrics 37 233

7 Covariant Differentiation and Geodesic Curves 40 243

8 Differential Geometry: Further Concepts 47 263

9 Curvature 55 284

10 Killing Vectors and Symmetries 64 315

11 Angular Momentum 67 327

12 Gravitation Generally 71 346

13 Gravitational Field Equations and Linearized Theory 76 364

14 Physics in Curved Spacetime 82 386

15 The Schwarzschild Geometry 87 404

16 Spherical Symmetry and Relativistic Stellar Structure 92 432

17 Black Holes 100 466

18 Gravitational Radiation 106 490

19 Cosmology 112 520

20 Experimental Tests 122 560

21 Miscellaneous 125 575

INDEX 593