Abstract
We shall not manipulate tensors very extensively in this book. Nevertheless tensors are indispensable for any genuine understanding of GR. Even the field equations cannot be expressed without them. In this section we sketch out the basic tensor theory as far as we shall need it. That includes the metric tensor, the geodesic equations, the absolute derivative, and the curvature tensor. The reader may skim it lightly at first, and refer back to it as need arises.
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References
For a rigorous proof, see W. B. Bonnor’s article in Recent Developments in General Relativity, p. 167, New York, Pergamon Press, Inc., 1962.
These may be found, for example, in A. S. Eddington, The Mathematical Theory of Relativity, Section 39, Cambridge University Press, 1924.
See, for example, H. P. Robertson and T. W. Noonan, Relativity and Cosmology, Section 9.6, W. B. Saunders Co., 1968.
A. Hall, Astron. J. 14, 49 (1894).
J. L. Anderson, Principles of Relativity Physics, New York, Academic Press, 1967.
See J. Mehra, Einstein, Hilbert, and the Theory of Gravitation, Reidel Pub. Co., 1974, especially p. 25.
Cf. W. Rindler, Phys. Rev. 120, 1041 (1960).
See A. S. Eddington, Space, Time, and Gravitation, Chapter X, Cambridge University Press, 1920 (and New York, Harper Torchbooks, 1959). Also Eddington, loc. cit. (Mathematical Theory) p. 166.
See L. Bass and F. A. E. Pirani, Philos. Mag. 46, 850 (1955).
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© 1977 Wolfgang Rindler
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Rindler, W. (1977). Formal Development of General Relativity. In: Essential Relativity. Text and Monographs in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-86650-0_8
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DOI: https://doi.org/10.1007/978-3-642-86650-0_8
Publisher Name: Springer, Berlin, Heidelberg
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