Conformally flat spherically symmetric spacetimes
Department of Engineering, Oslo University College, P.O.Box 4 St.Olavs Plass, N-0130, Oslo, Norway
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Accepted: 19 July 2013
Published online: 16 August 2013
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.
© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg, 2013