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Gravitational metrics of spherical symmetry and class one

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Summary

It is shown that every gravitational metric of spherical symmetry is in general of class two. A necessary and sufficient condition for the metric to be of class one is obtained in several forms. The limitations imposed by the condition on possible perfect fluid distributions are discussed.

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References

  1. Eisenhart, L. P.Riemannian Geometry, 1926, 189.

  2. Tolman, R. C.Relativity, Thermodynamics and Cosmology, 1934, 337–46.

  3. Weatherburn, C. E.Riemannian Geometry, 1942, 117.

  4. Eisenhart, L. P.Ibid., Riemannian Geometry, 197.

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Authors and Affiliations

  1. Benares Hindu University, India

    K. R. Karmarkar

Authors
  1. K. R. Karmarkar
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Additional information

(Communicated by Prof. V. V. Narlikar, F.A.Sc.)

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Karmarkar, K.R. Gravitational metrics of spherical symmetry and class one. Proc. Indian Acad. Sci. 27, 56 (1948). https://doi.org/10.1007/BF03173443

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  • DOI: https://doi.org/10.1007/BF03173443

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