General Relativity
A Graduate Course

A text on general relativity and its modern applications for an intensive one-semester Ph.D.-level course in physics.

Horatiu Nastase (Author)

9781009575751, Cambridge University Press

Hardback, published 8 May 2025

402 pages
26 x 18.5 x 2.8 cm, 0.91 kg

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. Assuming knowledge of classical mechanics and electromagnetism at an advanced undergraduate level, basic concepts are introduced quickly, with greater emphasis on their applications. Standard topics are covered, such as the Schwarzschild solution, classical tests of general relativity, gravitational waves, ADM parametrization, relativistic stars and cosmology, as well as more advanced standard topics like vielbein-spin connection formulation, trapped surfaces, the Raychaudhuri equation, energy conditions, the Petrov and Bianchi classifications and gravitational instantons. More modern topics, including black hole thermodynamics, gravitational entropy, effective field theory for gravity, the PPN expansion, the double copy and fluid-gravity correspondence, are also introduced using the language understood by physicists, without too abstract mathematics, proven theorems, or the language of pure mathematics.

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.

Subject Areas: Atmospheric physics [PHVJ]