Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-24T12:42:30.734Z Has data issue: false hasContentIssue false

Two bodies at rest in general relativity

Published online by Cambridge University Press:  24 October 2008

L. Marder
Affiliation:
King's CollegeLondon*

Abstract

It is well known that there is no static axisymmetric two-body solution of Einstein's gravitational field equations, if it is assumed that the bodies are separated in a certain definite sense. In this paper it is shown, by the construction of a complete physically sensible model, that static two-body solutions do exist for systems in which one body is hollow and contains the other. The stability of the particular system described is briefly discussed.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1959

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Bergmann, P. G.Introduction to the theory of relativity (New York, 1942), 208.Google Scholar
(2)Bondi, H.Rev. Mod. Phys. 29 (1957), 423.CrossRefGoogle Scholar
(3)Curzon, H. E. J.Proc. Lond. Math. Soc. (2), 23 (1924), 477.Google Scholar
(4)Einstein, A., Infeld, L. and Hoffman, B.Ann. Math. 39 (1938), 65.CrossRefGoogle Scholar
(5)Einstein, A. and Rosen, N.Phys. Rev. 49 (1936), 404.CrossRefGoogle Scholar
(6)Fock, V. A.Rev. Mod. Phys. 29 (1957), 325.CrossRefGoogle Scholar
(7)Levi-Civita, T.R. G. Accad. Lincei, 28 (1919), 3.Google Scholar
(8)Lichnerowicz, A.Theories relativistes de la gravitation et de l'électromagnetisme (Paris, 1955), Chapters I and III.Google Scholar
(9)Silberstein, L.Phys. Rev. 49 (1936), 268.CrossRefGoogle Scholar
(10)Takeno, H.Prog. Theor. Phys. 8 (1952), 317.CrossRefGoogle Scholar
(11)Tolman, R. C.Relativity, thermodynamics and cosmology (Oxford, 1934), 235.Google Scholar
(12)Weyl, H.Ann. Phys., Lpz., 54 (1917), 117.CrossRefGoogle Scholar
(13)Weyl, H.Math. Z. 13 (1922), 142.Google Scholar