http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
an introduction to Einstein's general relativity
Providing relevant solutions of the Einstein equation, this text introduces field equations of general relativity & their supporting mathematics. Emphasis is on the connection between observation & theory and the phenomena of gravitational physics.
Part I. Space and Time in Newtonian Physics and Special Relativity -- 1. Gravitational Physics -- 2. Geometry as Physics -- 2.1. Gravity Is Geometry -- 2.2. Experiments in Geometry -- 2.3. Different Geometries -- 2.4. Specifying Geometry -- 2.5. Coordinates and Line Element -- 2.6. Coordinates and Invariance -- 3. Space, Time, and Gravity in Newtonian Physics -- 3.1. Inertial Frames -- 3.2. The Principle of Relativity -- 3.3. Newtonian Gravity -- 3.4. Gravitational and Inertial Mass -- 3.5. Variational Principle for Newtonian Mechanics -- 4. Principles of Special Relativity -- 4.1. The Addition of Velocities and the Michelson-Morley Experiment -- 4.2. Einstein's Resolution and Its Consequences -- 4.3. Spacetime -- 4.4. Time Dilation and the Twin Paradox -- 4.5. Lorentz Boosts -- 4.6. Units -- 5. Special Relativistic Mechanics -- 5.1. Four-Vectors -- 5.2. Special Relativistic Kinematics -- 5.3. Special Relativistic Dynamics -- 5.4. Variational Principle for Free Particle Motion -- 5.5. Light Rays -- 5.6. Observers and Observations -- Part II. The Curved Spacetimes of General Relativity -- 6. Gravity as Geometry -- 6.1. Testing the Equality of Gravitational and Inertial Mass -- 6.2. The Equivalence Principle -- 6.3. Clocks in a Gravitational Field -- 6.4. The Global Positioning System -- 6.5. Spacetime Is Curved -- 6.6. Newtonian Gravity in Spacetime Terms -- 7. The Description of Curved Spacetime -- 7.1. Coordinates -- 7.2. Metric -- 7.3. The Summation Convention -- 7.4. Local Inertial Frames -- 7.5. Light Cones and World Lines -- 7.6. Length, Area, Volume, and Four-Volume for Diagonal Metrics -- 7.7. Embedding Diagrams and Wormholes -- 7.8. Vectors in Curved Spacetime -- 7.9. Three-Dimensional Surfaces in Four-Dimensional Spacetime -- 8. Geodesics -- 8.1. The Geodesic Equation -- 8.2. Solving the Geodesic Equation -- Symmetries and Conservation Laws -- 8.3. Null Geodesics -- 8.4. Local Inertial Frames and Freely Falling Frames -- 9. The Geometry Outside a Spherical Star -- 9.1. Schwarzschild Geometry -- 9.2. The Gravitational Redshift -- 9.3. Particle Orbits -- Precession of the Perihelion -- 9.4. Light Ray Orbits -- The Deflection and Time Delay of Light -- 10. Solar System Tests of General Relativity -- 10.1. Gravitational Redshift -- 10.2. PPN Parameters -- 10.3. Measurements of the PPN Parameter [gamma] -- 10.4. Measurement of the PPN Parameter [beta] -- Precession of Mercury's Perihelion -- 11. Relativistic Gravity in Action -- 11.1. Gravitational Lensing -- 11.2. Accretion Disks Around Compact Objects -- 11.3. Binary Pulsars -- 12. Gravitational Collapse and Black Holes -- 12.1. The Schwarzschild Black Hole -- 12.2. Collapse to a Black Hole -- 12.3. Kruskal-Szekeres Coordinates -- 12.4. Nonspherical Gravitational Collapse -- 13. Astrophysical Black Holes -- 13.1. Black Holes in X-Ray Binaries -- 13.2. Black Holes in Galaxy Centers -- 13.3. Quantum Evaporation of Black Holes -- Hawking Radiation -- 14. A Little Rotation -- 14.1. Rotational Dragging of Inertial Frames -- 14.2. Gyroscopes in Curved Spacetime -- 14.3. Geodetic Precession -- 14.4. Spacetime Outside a Slowly Rotating Spherical Body -- 14.5. Gyroscopes in the Spacetime of a Slowly Rotating Body -- 14.6. Gyros and Freely Falling Frames -- 15. Rotating Black Holes -- 15.1. Cosmic Censorship -- 15.2. The Kerr Geometry -- 15.3. The Horizon of a Rotating Black Hole -- 15.4. Orbits in the Equatorial Plane -- 15.5. The Ergosphere -- 16. Gravitational Waves -- 16.1. A Linearized Gravitational Wave -- 16.2. Detecting Gravitational Waves -- 16.3. Gravitational Wave Polarization -- 16.4. Gravitational Wave Interferometers -- 16.5. The Energy in Gravitational Waves -- 17. The Universe Observed -- 17.1. The Composition of the Universe -- 17.2. The Expanding Universe -- 17.3. Mapping the Universe -- 18. Cosmological Models -- 18.1. Homogeneous, Isotropic Spacetimes -- 18.2. The Cosmological Redshift -- 18.3. Matter, Radiation, and Vacuum -- 18.4. Evolution of the Flat FRW Models -- 18.5. The Big Bang and Age and Size of the Universe -- 18.6. Spatially Curved Robertson-Walker Metrics -- 18.7. Dynamics of the Universe -- 19. Which Universe and Why? -- 19.1. Surveying the Universe -- 19.2. Explaining the Universe -- Part III. The Einstein Equation -- 20. A Little More Math -- 20.1. Vectors -- 20.2. Dual Vectors -- 20.3. Tensors -- 20.4. The Covariant Derivative -- 20.5. Freely Falling Frames Again -- 21. Curvature and the Einstein Equation -- 21.1. Tidal Gravitational Forces -- 21.2. Equation of Geodesic Deviation -- 21.3. Riemann Curvature -- 21.4. The Einstein Equation in Vacuum -- 21.5. Linearized Gravity -- 22. The Source of Curvature -- 22.1. Densities -- 22.2. Conservation -- 22.2. Conservation of Energy-Momentum -- 22.3. The Einstein Equation -- 22.4. The Newtonian Limit -- 23. Gravitational Wave Emission -- 23.1. The Linearized Einstein Equation with Sources -- 23.2. Solving the Wave Equation with a Source -- 23.3. The General Solution of Linearized Gravity -- 23.4. Production of Weak Gravitational Waves -- 23.5. Gravitational Radiation from Binary Stars -- 23.6. The Quadrupole Formula for the Energy Loss in Gravitational Waves -- 23.7. Effects of Gravitational Radiation Detected in a Binary Pulsar -- 23.8. Strong Source Expectations -- 24. Relativistic Stars -- 24.1. The Power of the Pauli Principle -- 24.2. Relativistic Hydrostatic Equilibrium -- 24.3. Stellar Models -- 24.4. Matter in Its Ground State -- 24.5. Stability -- 24.6. Bounds on the Maximum Mass of Neutron Stars -- A. Units -- A.1. Units in General -- A.2. Units Employed in this Book -- B. Curvature Quantities -- C. Curvature and the Einstein Equation -- D. Pedagogical Strategy -- D.1. Pedagogical Principles -- D.2. Organization -- D.3. Constructing Courses.
Includes bibliographical references (pages 563-567) and index.