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Foliation of the Kottler–Schwarzschild–de Sitter spacetime by flat spacelike hypersurfaces

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Abstract

There exist Kruskal like coordinates for the Reissner–Nordstrom (RN) black hole spacetime which are regular at coordinate singularities. Non-existence of such coordinates for the extreme RN black hole spacetime has already been shown. Also the Carter coordinates available for the extreme case are not manifestly regular at the coordinate singularity, therefore, a numerical procedure was developed to obtain free fall geodesics and flat foliation for the extreme RN black hole spacetime. The Kottler–Schwarzschild–de Sitter (KSSdS) spacetime geometry is similar to the RN geometry in the sense that, like the RN case, there exist non-singular coordinates when there are two distinct coordinate singularities. There are no manifestly regular coordinates for the extreme KSSdS case. In this paper foliation of all the cases of the KSSdS spacetime by flat spacelike hypersurfaces is obtained by introducing a non-singular time coordinate.

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Authors and Affiliations

  1. Department of Basic Science and Humanities, EME College, National University of Science and Technology, Peshawar Road, Rawalpindi, Pakistan

    Azad A. Siddiqui

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  1. Azad A. Siddiqui
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Correspondence to Azad A. Siddiqui.

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Siddiqui, A.A. Foliation of the Kottler–Schwarzschild–de Sitter spacetime by flat spacelike hypersurfaces. Gen Relativ Gravit 43, 1189–1196 (2011). https://doi.org/10.1007/s10714-010-1064-7

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  • DOI: https://doi.org/10.1007/s10714-010-1064-7

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