| >>Note: Suitable for a one-semester course in general relativity for senior undergraduates or beginning graduate students, this text clarifies the mathematical aspects of Einstein's theory of relativity without sacrificing physical understanding. |
| The text begins with an exposition of those aspects of tensor calculus and differential geometry needed for a proper treatment of the subject. The discussion then turns to the spacetime of general relativity and to geodesic motion. A brief consideration of the field equations is followed by a discussion of physics in the vicinity of massive objects, including an elementary treatment of black holes and rotating objects. The main text concludes with introductory chapters on gravitational radiation and cosmology. |
| This new third edition has been updated to take account of fresh observational evidence and experiments. It includes new sections on the Kerr solution (in Chapter 4) and cosmological speeds of recession (in Chapter 6). A more mathematical treatment of tensors and manifolds, included in the 1st edition, but omitted in the 2nd edition, has been restored in an appendix. Also included are two additional appendixes - "Special Relativity Review" and "The Chinese Connection" - and outline solutions to all exercises and problems, making it especially suitable for private study. |
| | Lanchester’s transporter on a plane |
| | Lanchester’s transporter on a surface |
| | A trip at constant latitude |
| | Field equations and curvature |
| | The stress tensor and fluid motion |
| | The curvature tensor and related tensors |
| | Curvature and parallel transport |
| | Einstein’s field equations |
| | Einstein’s equation compared with Poisson’s equation |
| | The Schwarzschild solution |
| | Physics in the vicinity of a massive object |
| | Simple generation and detection |
| | Special relativity review |
| | The spacetime of general relativity and paths of particles |
| | A Short Course in General Relativity |
| | James Foster, J. David Nightingale |
| | Coordinate systems in Euclidean space |
| | Coordinate transformations in Euclidean space |
| | Tensor fields in Euclidean space |
| | Surfaces in Euclidean space |
| | Tensor fields on manifolds |
| | What and where are the bases? |
| | A Short Course in General Relativity |
| | James Foster, J. David Nightingale |
| | The spacetime of general relativity and paths of particles |
| | A rotating reference system |
| | Newton’s law of universal gravitation |
| | Gravitational potential and the geodesic |
| | The spacetime of general relativity |
| | Absolute and covariant differentiation |
| | Parallel vectors along a curve |
| | A Short Course in General Relativity |
| | James Foster, J. David Nightingale |
| | Physics in the vicinity of a massive object |
| | General particle motion (including photons) |
| | Rotating objects; the Kerr solution |
| | A Short Course in General Relativity |
| | James Foster, J. David Nightingale |
| | From tensors to tensor fields |
| | The tangent space at each point of a manifold |
| | Tensor fields on a manifold |
| | A Short Course in General Relativity |
| | James Foster, J. David Nightingale |
| | Special relativity review |
| | Relativistic addition of velocities |
| | Time dilation, length contraction |
| | A Short Course in General Relativity |
| | James Foster, J. David Nightingale |
| | Robertson-Walker line element |
| | Redshift, distance, and speed of recession |
| | Objects with large redshifts |
| | Comment on Einstein’s models; inflation |
| | A Short Course in General Relativity |
| | James Foster, J. David Nightingale |
| |