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E-raamat: General Relativity: Analytic and Symbolic Problems with Mathematica

(Università di Roma Tor Vergata, Roma, Italy)
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This book provides General Relativity problems to be tackled both analytically and symbolically-numerically with the Mathematica software.



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.

A number of the Mathematica codes used in this book can be accessed online here; [ INSERT URL WHEN AVAILABLE]

Key Features:

• Promotes the "learning by doing" approach, guiding the student in the building of the mathematical apparatus necessary to solve problems in General Relativity.

• Encourages the development of analytical skills to address and solve specific and challenging problems in General Relativity.

• Develops symbolic-numerical skills to address problems (often already solved analytically) so that the reader is prepared to attack even more elaborate calculations in General Relativity.

Chapter 1: Tensor Calculus.
Chapter 2: Metric Geometry.
Chapter 3: Covariant Derivatives.
Chapter 4: Geodesics.
Chapter 5: Space-time Curvature.
Chapter 6: Equivalence Principle.
Chapter 7: Einstein Field Equations.
Chapter 8: Schwarzschild Geometry.
Chapter 9: Classical Tests of General Relativity.
Chapter 10: Linearized Gravity.
Chapter 11: Gravitational Waves.
Chapter 12: Schwarzschild Black Holes.
Chapter 13: Charged or Rotating BH's.
Chapter 14: Relativistic Hydrodynamics.
Chapter 15: Cosmology. Appendix A: Tensor Calculus: Solutions and MathCodes. Appendix B: Metric Geometry: Solutions and MathCodes. Appendix C: Covariant Derivatives: Solutions and MathCodes. Appendix D: Geodesics: Solutions and MathCodes. Appendix E: Space-time Curvature: Solutions and MathCodes. Appendix F: Equivalence Principle: Solutions and MathCodes. Appendix G: Einstein Field Equations: Solutions and MathCodes. Appendix H: Schwarzschild Geometry: Solutions and MathCodes. Appendix I: Classical Tests of General Relativity: Solutions and MatchCodes. Appendix J: Linearized Gravity: Solutions and MathCodes. Appendix K: Gravitational Waves: Solutions and MathCodes. Appendix L: Schwarzschild Black Holes: Solutions and MathCodes. Appendix M: Charged or Rotating BH's: Solutions and MathCodes. Appendix N: Relativistic Hydrodynamics: Solutions and MathCodes. Appendix O: Cosmology: Solutions and MathCodes. Index.

Nicola Vittorio is full professor of Cosmology at the Physics Department of the University of Rome Tor Vergata. He carried out theoretical studies in cosmology and in the formation and evolution of the large-scale structure of the universe. He published 250 articles on refereed journals, and he also was the organizer and the editor of several international conferences and conference proceedings. Nicola Vittorio is National Fellow of the Academy of Sciences of Turin, Distinguished Member of the Italian Physical Society, Member of the European Academy of Sciences and Arts, of the European Physical Society, of the International Astronomical Union, of the Italian Astronomical Society, and of the Italian Society for the Advancement of Science.
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