With Modern Applications in Cosmology
- INTRODUCTION: NEWTONIAN PHYSICS AND SPECIAL RELATIVITY
- Relativity Principles and Gravitation
- The Special Theory of Relativity
- THE MATHEMATICS OF THE GENERAL THEORY OF RELATIVITY
- Vectors, Tensors, and Forms
- Basis Vector Fields and the Metric Tensor
- Non-inertial Reference Frames
- Differentiation, Connections, and Integration
- Curvature
- EINSTEIN’S FIELD EQUATIONS
- Einstein’s Field Equations
- The Linear Field Approximation
- The Schwarzschild Solution and Black Holes
- COSMOLOGY
- Homogeneous and Isotropic Universe Models
- Universe Models with Vacuum Energy
- Anisotropic and Inhomogeneous Universe Models
- ADVANCED TOPICS
- Covariant Decomposition, Singularities, and Canonical Cosmology
- Spatially Homogeneous Universe Models
- Israel’s Formalism: The Metric Junction Method
- Brane-worlds
- Kaluza-Klein Theory
- APPENDICES
- A – Constants of Nature
- B – Penrose Diagrams
- Conformal transformations and causal structure
- Schwarzschild spacetime
- de Sitter spacetime
- C – Anti-de Sitter Spacetime
- The anti-de Sitter hyperboloid
- Foliations of AdSn
- Geodesics in AdSn
- The BTZ black hole
- AdS3 as the group SL(2,R)