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

Derek F. Lawden: Tensor Calculus and Relativity (3rd Edition)

Published $\text {1975}$, Chapman and Hall

ISBN 0 412 20370 7

Subject Matter

• Relativity Theory

Contents

Preface (September 1960)

Preface to the Second Edition (September 1966)

Note on the 1975 Impression (February 1975)

$1$. 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

Next

Further Editions

• 1962: Derek F. Lawden: Tensor Calculus and Relativity
• 1968: Derek F. Lawden: Tensor Calculus and Relativity (2nd ed.)

Source work progress

• 1975: Derek F. Lawden: Tensor Calculus and Relativity (3rd ed.) ... (previous) ... (next): Chapter $1$ Special Principle of Relativity. Lorentz Transformations: $1$. Newton's laws of motion