General relativity : an introduction to black holes, gravitational waves, and cosmology / Michael J.W. Hall.

Περιλαμβάνει βιβλιογραφικές παραπομπές.

1. Concepts in special relativity -- 1.1. Galilean relativity -- 1.2. Inertial frames -- 1.3. Special relativity -- 1.4. Velocity addition, length contraction, and time dilation -- 1.5. Questions

2. Tensors in relativity -- 2.1. Motivation -- 2.2. General tensors and their basic properties -- 2.3. Lorentz tensors -- 2.4. Example : 4-momentum and force -- 2.5. Example : Doppler effect -- 2.6. Questions

3. The equivalence principle and local inertial frames -- 3.1. Inertial versus gravitational mass -- 3.2. Einstein's equivalence principle -- 3.3. Local inertial frames -- 3.4. Questions

4. The motion of freely falling particles in general relativity -- 4.1. Local inertial frames and the geodesic equation -- 4.2. The metric tensor -- 4.3. Gravity as geometry -- 4.4. The Newtonian limit -- 4.5. Questions

5. The Schwarzschild metric and black holes -- 5.1. Spherical symmetry and the Schwarzschild metric -- 5.2. Geodesics in spherically symmetric spacetimes -- 5.3. Particle geodesics in a Schwarzschild spacetime -- 5.4. Deflection of light by the Sun -- 5.5. Falling into a black hole -- 5.6. Questions

6. Tensors and geometry -- 6.1. Covariant derivatives -- 6.2. Basic properties of covariant derivatives -- 6.3. Riemann and Ricci tensors -- 6.4. Symmetries and Bianchi identities -- 6.5. Questions

7. Einstein's field equations -- 7.1. Overview -- 7.2. Energy-momentum tensor and conservation laws -- 7.3. The field equations for general relativity -- 7.4. The cosmological constant -- 7.5. Questions

8. Solving the field equations : vacuum solutions -- 8.1. The vacuum field equations -- 8.2. The Schwarzschild-de Sitter solution -- 8.3. Gravitational waves -- 8.4. Questions

9. Solving the field equations : cosmological solutions -- 9.1. The cosmological principle -- 9.2. The Friedmann-Robertson-Walker metric -- 9.3. Friedmann-Robertson-Walker universes -- 9.4. Questions

Appendices. A. Derivation of Lorentz transformations -- B. Derivation of Einstein's field equations -- C. Remarks on selected questions.

General Relativity: An Introduction to Black Holes, Gravitational Waves, and Cosmology provides readers with a solid understanding of the underlying physical concepts of general relativity. It also shows how they may derive important applications of the theory and is a solid grounding for those wishing to pursue further study. This thorough primer is based on class-tested undergraduate lectures from Griffith University, Brisbane. It develops the basic elements of general relativity with applications to the gravitational deflection of light, GPS, black holes, gravitational waves, and cosmology.