Book:Derek F. Lawden/Tensor Calculus and Relativity/Third Edition

Subject Matter

 * Relativity Theory

Contents

 * Preface


 * $1$. Special Principle of Relativity. Lorentz Transformations
 * 1. Newton's laws of motion
 * 2. Covariance of the laws of motion
 * 3. Special principle of relativity
 * 4. Lorentz transformations. Minkowski space-time
 * 5. The special Lorentz transformation
 * 6. Fitzgerald contraction. Time dilation
 * 7. Spacelike and timelike intervals. Light cone
 * Exercises $1$


 * $2$. Orthogonal Transformations. Cartesian Tensors
 * 8. Orthogonal transformations
 * 9. Repeated index summation convention
 * 10. Rectangular Cartesian tensors
 * 11. Invariants. Gradients. Derivatives of tensors
 * 12. Contraction. Scalar product. Divergence
 * 13. Tensor densities
 * 14. Vector products. Curl
 * Exercises $2$


 * $3$. Special Relativity Mechanics
 * 15. The velocity vector
 * 16. Mass and momentum
 * 17. The force vector. Energy
 * 18. Lorentz transformation equations for force
 * 19. Motion with variable proper mass
 * 20. Lagrange's and Hamilton's equations
 * Exercises $3$


 * $4$. Special Relativity Electrodynamics
 * 21. $4$-Current Density
 * 22. $4$-Vector potential
 * 23. The field tensor
 * 24. Lorentz transformations of electric and magnetic intensities
 * 25. The Lorentz force
 * 26. Force density
 * 27. The energy-momentum tensor for an electromagnetic field
 * 28. Equations of motion of a charge flow
 * Exercises $4$


 * $5$. General Tensor Calculus. Riemannian Space
 * 29. Generalized $N$-dimensional spaces
 * 30. Contravariant and covariant tensors
 * 31. The quotient theorem. Conjugate tensors
 * 32. Relative tensors and tensor densities
 * 33. Covariant derivatives. Parallel displacement. Affine connection
 * 34. Transformation of an affinity
 * 35. Covariant derivatives of tensors
 * 36. Covariant differentiation of relative tensors
 * 37. The Riemann-Christoffel curvature tensor
 * 38. Geodesic coordinates. The Bianchi identities
 * 39. Metrical connection. Raising and lowering of indices
 * 40. Scalar products. Magnitudes of vectors
 * 41. The Christoffel symbols. Metric affinity
 * 42. The covariant curvature tensor
 * 43. Divergence. The Laplacian. Einstein's tensor
 * 44. Geodesics
 * Exercises $5$


 * $6$. General Theory of Relativity
 * 45. Principle of equivalence
 * 46. Metric in a gravitational field
 * 47. Motion of a free particle in a gravitational field
 * 48. Einstein's law of gravitation
 * 49. Acceleration of a particle in a weak gravitational field
 * 50. Newton's law of gravitation
 * 51. Metrics with spherical symmetry
 * 52. Schwarzchild's solution
 * 53. Planetary orbits
 * 54. Gravitational deflection of a light ray
 * 55. Gravitational displacement of spectral lines
 * 56. Maxwell's equations in a gravitational field
 * Exercises $6$


 * Miscellaneous Problems


 * Appendix Bibliography


 * Index