General Relativity Analytic and Symbolic Problems with Mathematica

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.         

Biography

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.

An original and timely textbook, General Relativity: Problems and Solutions with Mathematica by Nicola Vittorio combines analytical rigor with the power of symbolic manipulation software to tackle a wide range of problems in Einstein’s theory of gravity. It offers a truly “hands-on” approach to learning general relativity, guiding readers through both the conceptual and technical aspects of the subject while introducing advanced features of Wolfram Mathematica.

General Relativity often involves laborious but conceptually straightforward computations that can obscure physical insight. This book succeeds in cutting through the algebraic complexity, allowing students to focus on the core ideas while still engaging with the full mathematical machinery. The accompanying notebooks are carefully crafted to develop symbolic-numerical skills and foster a deeper understanding of the theory.

A highly valuable resource for advanced undergraduates, graduate students, and anyone seeking a practical and modern way to approach general relativity. A must-read for every scholar in the field.

- Paolo Pani, Sapienza University of Rome, July 2025