General Relativity for the Gifted Amateur

Tom Lancaster, Professor of Physics, University of Durham,Stephen Blundell, Professor of Physics, University of Oxford

Tom Lancaster is Professor of Physics at Durham University. His research interests include using muons to investigate low-dimensional and molecular magnetism.


Stephen Blundell is a Professor of Physics at the University of Oxford, and a Professorial Fellow of Mansfield College. His research interests include muon-spin rotation, density functional techniques, and spin liquids.

0. OvertureI Geometry and mechanics in at spacetime1. Special relativity2. Vectors in at spacetime3. Coordinates4. Linear slot machines5. The metricII Curvature and general relativity6. Finding a theory of gravitation7. Parallel lines and the covariant derivative8. Free fall and geodesics9. Geodesic equations and connection coecients10. Making measurements in relativity11. Riemann curvature and the Ricci tensor12. The energy-momentum tensor13. The gravitational field equations14. The triumphs of general relativityIII Cosmology15. An introduction to cosmology16. Robertson-Walker spaces17. The Friedmann equations18. Universes of the past and future19. Causality, infinity and horizonsIV Orbits, stars and black holes20. Newtonian orbits21. The Schwarzschild geometry22. Motion in the Schwarzschild geometry23. Orbits in the Schwarzschild geometry24. Photons in the Schwarzschild geometry25. Black holes26. Black-hole singularities27. Kruskal-Szekeres coordinates28. Hawking radiation29. Charged and rotating black holesV Geometry30. Classical curvature31. A reintroduction to geometry32. Differential forms33. Exterior and Lie derivatives34. Geometry of the connection35. Riemann curvature revisited36. Cartan's method37. Duality and the volume form38. Forms, chains and Stokes' theoremVI Classical and quantum fields39. Fluids as dry water40. Lagrangian field theory41. Inflation42. The electromagnetic field43. Charge conservation and the Bianchi identity44. Gauge fields45. Weak gravitational fields46. Gravitational waves47. The properties of gravitons48. Higher-dimensional spacetime49. From classical to quantum gravity50. The Big-Bang singularityA. Further readingB. Conventions and notationC. Manifolds and bundlesD. EmbeddingE. Answers to selected problems