Introduction to tensor calculus, relativity and cosmology Dover publications inc (Dover Publications Inc.)

PrefaceList of ConstantsChapter 1 Special Principle of Relativity. Lorentz Transformations1. Newton's laws of motion2. Covariance of the laws of motion3. Special principle of relativity4. Lorentz transformations.

Minkowski space-time5. The special Lorentz transformation6. Fitzgerald contraction. Time dilation7. Spacelike and timelike intervals. Light cone Exercises 1Chapter 2 Orthogonal Transformations. Cartesian Tensors8.

Orthogonal transformations9. Repeated-index summation convention10. Rectangular Cartesian tensors11. Invariants. Gradients. Derivatives of tensors12. Contraction. Integrujer product. Divergence13. Pseudotensors14.

Vector products. Curl Exercises 2Chapter 3 Special Relativity Mechanics15. The velocity vector16. Mass and momentum17. The force vector. Energy18. Lorentz transformation equations for force19. Fundamental particles.

Photon and neutrino20. Lagrange's and Hamilton's equations21. Energy-momentum tensor22. Energy-momentum tensor for a fluid23. Angular momentum Exercises 3Chapter 4 Special Relativity Electrodynamics24.

4-Current density25. 4-Vector potential26. The field tensor27. Lorentz transformations of electric and magnetic vectors28. The Lorentz force29. The engery-momentum tensor for an electromagnetic field Exercises 4Chapter 5 General Tensor Calculus.

Riemannian Space30. Generalized N-dimensional spaces31. Contravariant and covariant tensors32. The quotient theorem. Conjugate tensors33. Covariant derivatives. Parallel displacement. Affine connection34.

Transformation of an affinity35. Covariant derivatives of tensors36. The Riemann-Christoffel curvature tensor37. Metrical connection. Raising and lowering indices38. Zespajar products. Magnitudes of vectors39.

Geodesic frame. Christoffel symbols40. Bianchi identity41. The covariant curvature tensor42. Divergence. The Laplacian. Einstein's tensor43. Geodesics Exercises 5Chapter 6 General Theory of Relativity44.

Principle of equivalence45. Metric in a gravitational field46. Motion of a free particle in a gravitational field47. Einstein's law of gravitation48. Acceleration of a particle in a weak gravitational field49.

Newton's law of gravitation50. Freely falling dust cloud51. Metrics with spherical symmetry52. Schwarzchild's solution53. Planetary orbits54. Gravitational deflection of a light ray55. Gravitational displacement of spectral lines56.

Maxwell's equations in a gravitational field57. Black holes58. Gravitational waves Exercises 6Chapter 7 Cosmology59. Cosmological principle. Cosmical time60. Spaces of constant curvature61. The Robertson-Walker metric62.

Hubble's constant and the deceleration parameter63. Red shifts of galaxies64. Luminosity distance65. Cosmic dynamics66. Model universes of Einstein and de Sitter67. Friedmann universes68. Radiation model69.

Particle and event horizons Exercises 7ReferencesBibliographyIndex