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## Overview

This elementary introduction pays special attention to aspects of tensor calculus and relativity that students tend to find most difficult. Its use of relatively unsophisticated mathematics in the early chapters allows readers to develop their confidence within the framework of Cartesian coordinates before undertaking the theory of tensors in curved spaces and its application to general relativity theory.

Topics include the special principle of relativity and Lorentz transformations; orthogonal transformations and Cartesian tensors; special relativity mechanics and electrodynamics; general tensor calculus and Riemannian space; and the general theory of relativity, including a focus on black holes and gravitational waves. The text concludes with a chapter offering a sound background in applying the principles of general relativity to cosmology. Numerous exercises advance the theoretical developments of the main text, thus enhancing this volume’s appeal to students of applied mathematics and physics at both undergraduate and postgraduate levels. Preface. List of Constants. References. Bibliography.

## Product Details

ISBN-13: | 9780486425405 |
---|---|

Publisher: | Dover Publications |

Publication date: | 01/27/2003 |

Series: | Dover Books on Physics Series |

Edition description: | 3RD |

Pages: | 224 |

Sales rank: | 370,874 |

Product dimensions: | 6.14(w) x 9.21(h) x (d) |

## Table of Contents

Preface

List of Constants

Chapter 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

Chapter 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. Pseudotensors

14. Vector products. Curl

Exercises 2

Chapter 3 Special Relativity Mechanics

15. The velocity vector

16. Mass and momentum

17. The force vector. Energy

18. Lorentz transformation equations for force

19. Fundamental particles. Photon and neutrino

20. Lagrange's and Hamilton's equations

21. Energy-momentum tensor

22. Energy-momentum tensor for a fluid

23. Angular momentum

Exercises 3

Chapter 4 Special Relativity Electrodynamics

24. 4-Current density

25. 4-Vector potential

26. The field tensor

27. Lorentz transformations of electric and magnetic vectors

28. The Lorentz force

29. The engery-momentum tensor for an electromagnetic field

Exercises 4

Chapter 5 General Tensor Calculus. Riemannian Space

30. Generalized N-dimensional spaces

31. Contravariant and covariant tensors

32. The quotient theorem. Conjugate tensors

33. Covariant derivatives. Parallel displacement. Affine connection

34. Transformation of an affinity

35. Covariant derivatives of tensors

36. The Riemann-Christoffel curvature tensor

37. Metrical connection. Raising and lowering indices

38. Scalar products. Magnitudes of vectors

39. Geodesic frame. Christoffel symbols

40. Bianchi identity

41. The covariant curvature tensor

42. Divergence. The Laplacian. Einstein's tensor

43. Geodesics

Exercises 5

Chapter 6 General Theory of Relativity

44. Principle of equivalence

45. Metric in a gravitational field

46. Motion of a free particle in a gravitational field

47. Einstein's law of gravitation

48. Acceleration of a particle in a weak gravitational field

49. Newton's law of gravitation

50. Freely falling dust cloud

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

57. Black holes

58. Gravitational waves

Exercises 6

Chapter 7 Cosmology

59. Cosmological principle. Cosmical time

60. Spaces of constant curvature

61. The Robertson-Walker metric

62. Hubble's constant and the deceleration parameter

63. Red shifts of galaxies

64. Luminosity distance

65. Cosmic dynamics

66. Model universes of Einstein and de Sitter

67. Friedmann universes

68. Radiation model

69. Particle and event horizons

Exercises 7

References

Bibliography

Index