Abstract
In Chapter 3 we obtained the static spherically symmetric solution of Schwarzschild, and identified it as representing the gravitational field surrounding a spherically symmetric body of mass M situated in an otherwise empty spacetime. This solution is asymptotically flat, and in no way incorporates the gravitational effects of distant matter in the Universe. Nevertheless, it seems reasonable to adopt it as a model for the gravitational field in the vicinity of a spherical massive object such as a star, where the star’s mass is the principal contributor to the gravitational field.
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References
They could therefore be the tests of any other theory of gravitation which yielded the Schwarzschild solution. See also Biswas, 1994.
See Shapiro, 1964.
See Shapiro, 1968; Shapiro et al., 1971; and Anderson et al., 1975.
See Pound and Rebka, 1960.
See, Møller, 1972, §12.2.
The intention here is to make clear what is small and what is not by using dimensionless quantities and variables that do not depend on the units used. The constant u0 is taken as a characteristic value for u and is used to define the variable ū, whose value for nearly circular orbits is then not too different from unity. We are effectively scaling u, so that the problem is formulated in a dimensionless way. (The angular variable φ is already dimensionless.) See, for example Logan, 1987, §1.3.
The pulsar was discovered in 1975 by Hulse and Taylor. See Hulse and Taylor, 1975, and Weisberg and Taylor, 1984.
In 1911, prior to general relativity, Einstein predicted a deflection equal to half this amount. See Hoffman, 1972, Chap. 8, for history, and Kilmister, 1973, Extract 3, for a translation of Einstein’s paper.
See, for example, Riley, 1973, where references for other experiments are given.
See the paper by Everitt, Fairbank, and Hamilton in Carmeli et al., 1970.
In classical physics the escape velocity for a particle from a star of mass M and radius r is (2GM/r)1/2. Assigning a light corpuscle the escape velocity c yields r = 2GM/c2, which is also the Schwarzschild result. See Hawking and Ellis, 1973, Appendix A, for a translation of Laplace’s essay.
See, for example, Misner, Thorne, and Wheeler, 1973, §34.6.
See Thorne, 1974, and Young et al., 1978.
Discussed in, for example, Weinberg, 1972, §1.3.
See Thirring and Lense, 1918.
The derivation of this solution uses techniques that are beyond the scope of this introductory text. See Kerr, 1963.
See Boyer and Lindquist, 1967.
See Mach, 1893; also Weinberg, 1972, p.16.
See, for example, Misner, Thorne and Wheeler (1973), or Ohanian and Ruffini (1994).
See, for example, Shapiro and Teukolsky, 1983, p. 358.
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Foster, J., Nightingale, J.D. (2006). Physics in the vicinity of a massive object. In: A Short Course in General Relativity. Springer, New York, NY. https://doi.org/10.1007/978-0-387-27583-3_5
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DOI: https://doi.org/10.1007/978-0-387-27583-3_5
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