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Conformally flat spherically symmetric spacetimes

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Abstract

We deduce a simple expression for the Kretschmann curvature scalar of a conformally flat spacetime with a perfect fluid. Conformally flat, static, spherically symmetric spacetimes are investigated in various coordinate systems. The equation for a vanishing Weyl tensor and Einstein's field equations are integrated in curvature coordinates. We find conformally flat generalizations of the de Sitter spacetime and give new analyses of the internal Schwarzschild spacetime and texture-dominated spacetimes. The spacetimes are described in curvature coordinates, isotropic coordinates and in conformally flat spacetime coordinates.

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Authors and Affiliations

  1. Department of Engineering, Oslo University College, P.O.Box 4 St.Olavs Plass, N-0130, Oslo, Norway

    Øyvind Grøn & Steinar Johannesen

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  1. Øyvind Grøn
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  2. Steinar Johannesen
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Correspondence to Øyvind Grøn.

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Grøn, Ø., Johannesen, S. Conformally flat spherically symmetric spacetimes. Eur. Phys. J. Plus 128, 92 (2013). https://doi.org/10.1140/epjp/i2013-13092-2

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  • DOI: https://doi.org/10.1140/epjp/i2013-13092-2

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