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Description
This book provides General Relativity problems to be tackled both analytically and symbolically-numerically with the Mathematica software. In the first case, the reader is guided in setting up the appropriate solutions. In the second case, the reader is provided with very illustrative notebooks to carry out the steps necessary to solve a General Relativity problem. These include the calculation of the Christoffel symbols, Riemann, Ricci, Einstein and energy-momentum tensors, as well as the resolution of the field equations of General Relativity in different astrophysical/cosmological contexts, with and without the introduction of a cosmological constant. This study guide should be used alongside existing textbooks to provide additional learning and engagement opportunities for advanced undergraduate and graduate students in physics and astrophysics taking courses on general relativity. It may also be of interest to mathematics students interested in celestial mechanics and space sciences. Contents Preface Author Bio 1 Tensor Calculus 2 Metric Geometry 3 Covariant Derivatives 4 Geodesics 5 Space-time Curvature 6 Equivalence Principle 7 Einstein Field Equations 8 Schwarzschild Geometry 9 Classical Tests of General Relativity 10 Linearized Gravity 11 Gravitational Waves 12 Schwarzschild Black Holes 13 Charged or Rotating Black Holes 14 Relativistic Hydrodynamics 15 Cosmology Appendix A Appendix B Appendix C Appendix D Appendix E Appendix F Appendix G Appendix H Appendix I Appendix J Appendix K Appendix L Appendix M Appendix N Appendix O Index Related Topics Applied Mathematics |
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