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The relativistic incompressible sphere

Published online by Cambridge University Press:  09 April 2009

H. A. Buchdahl  and
W. J. Land
H. A. Buchdahl
Affiliation:
Australian National UniversityCanberra
W. J. Land
Affiliation:
Australian National UniversityCanberra
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Summary

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The Schwarzschild Interior Solution represents a static sphere the proper density of which has the same value throughout. Though it is sometimes referred to as an “incompressible” sphere it is physically unacceptable since (formally) the speed of sound within it is infinite. Perhaps the most natural analogue of the classical incompressible sphere is therefore a sphere such that the speed of sound is everywhere just equal to the speed of light. This paper investigates spheres of this kind in some detail.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 8 , Issue 1 , February 1968 , pp. 6 - 16
Copyright
Copyright © Australian Mathematical Society 1968

References

1 E.g., Tolman, R. C., Relativity, Thermodynamics and Cosmology (Clarendon Press, Oxford, 1934), Chap. 7, p. 245.Google Scholar

2 See the discussion of Synge: Synge, J. L., Relativity: The Special Theory (North-Holland Publishing Company, Amsterdam, 1958), Chap. 8, § 15, p. 306.Google Scholar

3 Units are such that the speed of light c and Newton's constant k both take the numerical value unity. The subscripts b and c refer to the boundary and centre of the sphere respectively.Google Scholar

4 Reference 2, p. 245. The cosmical constant is taken to be zero.Google Scholar

5 Buchdahl, H. A., Phys. Rev. 116 (1959), 1027. This paper will be referred to as I.CrossRefGoogle Scholar

6 Buchdahl, H. A., Astrophysical Journal, 146 (1966), 275.CrossRefGoogle Scholar