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Rotating fluid masses in general relativity

Published online by Cambridge University Press:  24 October 2008

R. H. Boyer
R. H. Boyer
Affiliation:
University of Liverpool
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Extract

In what follows we shall derive some properties of the gravitational field of an isolated, axially symmetric, uniformly rotating mass of perfect fluid in a steady state, according to the general theory of relativity. Several exact models describing rotating fluids are known in Newtonian mechanics, the Maclaurin and Jacobi ellipsoids ((6)) being perhaps the most interesting. In general relativity, no such exact solution is known in its entirety, although Kerr ((4)) has exhibited a certain vacuum solution possessing features that one might expect of a space-time exterior to some rotating body. Throughout this paper we shall have Kerr's solution in mind. The question that we shall keep before us is whether a perfect fluid interior can be matched to any given exterior field. Our main results exhibit the class of all possible fluid boundaries, given the exterior field, and some relations between the pressure, density, 4-velocity, and interior metric tensor.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 61 , Issue 2 , April 1965 , pp. 527 - 530
Copyright
Copyright © Cambridge Philosophical Society 1965

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References

REFERENCES

(1)Boyer, R. H. and Price, T. G.An interpretation of the Kerr metric in general relativity. Proc. Cambridge Philos. Soc. 61 (1965), 531.CrossRefGoogle Scholar
(2)Cattaneo, C.Dérivation transverse et grandeurs relatives en relativité générale. C.R. Acad. Sci., Paris, 248 (1959), 197–199.Google Scholar
(3)Cattaneo, C.Équation relativiste de Gauss–Poisson dans les univers statiques. C.R. Acad. Sci. Paris, 252 (1961), 2678–2680.Google Scholar
(4)Kerr, R. P.Gravitational field of a spinning mass as an example of algebraically special metrics. Phys. Rev. Lett. 9 (1963), 237–238.CrossRefGoogle Scholar
(5)Lichnerowicz, A.Théories relativistes de la gravitation et de l'éleclromagnétisme (Masson; Paris, 1955).Google Scholar
(6)Lyttleton, R. A.The stability of rotating liquid masses (Cambridge, 1953).Google Scholar
(7)Synge, J. L.Relativity: the special theory (North-Holland; Amsterdam, 1956).Google Scholar