This text on general relativity and its modern applications is suitable for an intensive one-semester course on general relativity, at the level of a Ph.D. student in physics. It covers basic and advanced standard topics, as well as modern topics using the language understood by physicists, without too abstract mathematics.
This text on general relativity and its modern applications is suitable for an intensive one-semester course on general relativity, at the level of a Ph.D. student in physics. It covers basic and advanced standard topics, as well as modern topics using the language understood by physicists, without too abstract mathematics.
Horäiu N¿stase is a researcher at the Institute for Theoretical Physics, State University of São Paulo. He completed his Ph.D. at Stony Brook with Peter van Nieuwenhuizen, co-discoverer of supergravity. While in Princeton as a postdoc, in a 2002 paper with David Berenstein and Juan Maldacena, he started the pp-wave correspondence, a sub-area of the AdS/CFT correspondence. He has written more than 100 scientific articles and 7 other books: Introduction to the AdS/CFT Correspondence (2015), String Theory Methods for Condensed Matter Physics (2017), Classical Field Theory (2019), Introduction to Quantum Field Theory (2019), Cosmology and String Theory (2019), Quantum Mechanics: A Graduate Course (2022) and Supergravity (2024).
Inhaltsangabe
1. General relativity, kinematics: metric, parallel transport, and general coordinate invariance 2. General relativity, dynamics: curvature, the Einstein-Hilbert action and the Einstein equation 3. Perturbative gravity: Fierz-Pauli action and gauge conditions 4. Gravitational waves: perturbation, exact solutions, generation, multipole expansion 5. Nonperturbative gravity: the vacuum Schwarzschild solution 6. Deflection of light by the Sun and comparison with special relativity 7. The other classical tests of general relativity: the gravitational redshift, the perihelion precession, the time delay of radar 8. Vielbein-spin connection formulation of general relativity gravity vs. gauge theory, in 4 dimensions and 3 dimensions 9. Gravity and geometry, Lovelock and Chern-Simons, topological terms, extensions, anomalies 10. The ADM parametrization and applications 11. Canonical formalism for gravity, Wheeler-de Wit equation, canonical quantization of gravity 12. Gravitoelectric and gravitomagnetic fields and applications 13. Penrose diagrams and black holes Schwarzschild example 14. Reissner-Nordstrom black hole spacetime and extremal black holes 15. Kerr and Kerr-Newman black hole spacetimes and the Penrose process 16. Trapped surfaces, event horizons, causality and topology 17. The Raychaudhuri equation 18. The laws of black hole thermodynamics and black hole radiation 19. Wald entropy and Sen's entropy function formalism 20. The energy conditions, singularity theorems, and wormholes 21. Relativistic stars and gravitational collapse to black holes 22. Effective field theory from gravity and black holes 23. General relativity solutions and the gauge theory double copy 24. The fluid-gravity correspondence 25. Fully linear gravity example: parallel plane (pp) wave and gravitational shockwave solutions 26. Dimensional reduction solutions: the domain wall, the cosmic string, and the 3-dimensional BTZ black hole solutions 27. Time-dependent gravity solutions: the Friedmann-Lemaître-Robertson-Walker (FLRW) cosmological solution, de Sitter and Anti-de Sitter cosmologies 28. General relativistic aspects of inflationary cosmology 29. The (Parametrized) Post-Newtonian expansion and metric frames 30. The Newman-Penrose formalism 31. The Petrov classification 32. The Bianchi classification of Lie algebras, Riemannian manifolds and cosmologies 33. Nontrivial topologies: Gravitational instantons, Taub-NUT, KK monopole and Gödel spacetimes References.
1. General relativity, kinematics: metric, parallel transport, and general coordinate invariance 2. General relativity, dynamics: curvature, the Einstein-Hilbert action and the Einstein equation 3. Perturbative gravity: Fierz-Pauli action and gauge conditions 4. Gravitational waves: perturbation, exact solutions, generation, multipole expansion 5. Nonperturbative gravity: the vacuum Schwarzschild solution 6. Deflection of light by the Sun and comparison with special relativity 7. The other classical tests of general relativity: the gravitational redshift, the perihelion precession, the time delay of radar 8. Vielbein-spin connection formulation of general relativity gravity vs. gauge theory, in 4 dimensions and 3 dimensions 9. Gravity and geometry, Lovelock and Chern-Simons, topological terms, extensions, anomalies 10. The ADM parametrization and applications 11. Canonical formalism for gravity, Wheeler-de Wit equation, canonical quantization of gravity 12. Gravitoelectric and gravitomagnetic fields and applications 13. Penrose diagrams and black holes Schwarzschild example 14. Reissner-Nordstrom black hole spacetime and extremal black holes 15. Kerr and Kerr-Newman black hole spacetimes and the Penrose process 16. Trapped surfaces, event horizons, causality and topology 17. The Raychaudhuri equation 18. The laws of black hole thermodynamics and black hole radiation 19. Wald entropy and Sen's entropy function formalism 20. The energy conditions, singularity theorems, and wormholes 21. Relativistic stars and gravitational collapse to black holes 22. Effective field theory from gravity and black holes 23. General relativity solutions and the gauge theory double copy 24. The fluid-gravity correspondence 25. Fully linear gravity example: parallel plane (pp) wave and gravitational shockwave solutions 26. Dimensional reduction solutions: the domain wall, the cosmic string, and the 3-dimensional BTZ black hole solutions 27. Time-dependent gravity solutions: the Friedmann-Lemaître-Robertson-Walker (FLRW) cosmological solution, de Sitter and Anti-de Sitter cosmologies 28. General relativistic aspects of inflationary cosmology 29. The (Parametrized) Post-Newtonian expansion and metric frames 30. The Newman-Penrose formalism 31. The Petrov classification 32. The Bianchi classification of Lie algebras, Riemannian manifolds and cosmologies 33. Nontrivial topologies: Gravitational instantons, Taub-NUT, KK monopole and Gödel spacetimes References.
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