- Access by Xinjiang University
Arbitrary Concentrations of Matter and the Schwarzschild Singularity
Phys. Rev. 89, 417 – Published 15 January, 1953
DOI: https://doi.org/10.1103/PhysRev.89.417
Abstract
A nonstatic solution of the Einstein gravitational equations representing a spherically symmetric cluster of radially moving particles in an otherwise empty space is obtained. While it has been presumed by Einstein that the Schwarzschild singularity is physically unattainable as matter cannot be concentrated arbitrarily, the present solution seems to show that there is no theoretical limit to the degree of concentration, and that the Schwarzschild singularity has no physical reality as it occurs only in some particular coordinate systems. Incidentally, it is shown that in case of spherical symmetry the condition of conservation of gravitational energy of an isolated system of fluid material is equivalent to the vanishing of pressure at the boundary.
References (16)
- A. Einstein, Ann. Math. 40, 922 (1939)
Omitted endnote
- R. Birkhoff, Relativity and Modern Physics (Harvard University Press, Cambridge, 1923), p. 253
- A. Einstein and E. G. Straus, Revs. Modern Phys. 17, 120 (1945) ibid.18, 148 (1946)
- G. Lemaitre, Ann. soc. sci. de Bruxelles, Ser. I 53, 51 (1933) J. L. Synge, Proc. Roy. Irish Acad. A53, 84-114 (1950)
- R. C. Tolman, Relativity, Thermodynamics and Cosmology (Oxford University Press, London, 1934), p. 252
Omitted endnote
- A. Einstein, The Meaning of Relativity (Methuen and Company, Ltd., London, 1950), fourth edition, p. 113
- M. Wyman, Phys. Rev. 70, 74 (1946)
Omitted endnote
Omitted endnote
- [6], p. 251
- P. G. Bergmann, Introduction to The Theory of Relativity (Prentice Hall, Inc., New York, 1947), p. 129
- J. L. Synge, Proc. Roy. Irish Acad. A53, 84 (1950), p. 107
- [6], p. 438
- [8], p. 118