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The relativistic incompressible sphere

  • H. A. Buchdahl (a1) and W. J. Land (a1)

Summary

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.

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Copyright

References

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

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

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.

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

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

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

* Physics Department, Harvard University, Cambridge, Mass.

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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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