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Regular spherical dust spacetimes

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Abstract

Physical (and weak) regularity conditions are used to determine and classify all the possible types of spherically symmetric dust spacetimes in general relativity. This work unifies and completes various earlier results. The junction conditions are described for general non-comoving (and non-null) surfaces, and the limits of kinematical quantities are given on all comoving surfaces where there is Darmois matching. We show that an inhomogeneous generalisation of the Kantowski-Sachs metric may be joined to the Lemaître-Tolman-Bondi metric. All the possible spacetimes are explicitly divided into four groups according to topology, including a group in which the spatial sections have the topology of a 3-torus. The recollapse conjecture (for these spacetimes) follows naturally in this approach.

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Acknowledgments

We thank Bill Bonnor and Charles Hellaby for helpful discussions. We thank Syksy Rasanen for reminding us about our original preprint. R. M. is supported by the South African Square Kilometre Array Project, the STFC (UK) (grant no. ST/H002774/1) and a Royal Society (UK)/ National Research Foundation (SA) exchange grant.

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Authors and Affiliations

  1. Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth, PO1 3FX, UK

    Neil P. Humphreys, Roy Maartens & David R. Matravers

  2. Physics Department, University of the Western Cape, Cape Town, 7535, South Africa

    Roy Maartens

Authors
  1. Neil P. Humphreys
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  2. Roy Maartens
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  3. David R. Matravers
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Correspondence to David R. Matravers.

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Humphreys, N.P., Maartens, R. & Matravers, D.R. Regular spherical dust spacetimes. Gen Relativ Gravit 44, 3197–3215 (2012). https://doi.org/10.1007/s10714-012-1452-2

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  • DOI: https://doi.org/10.1007/s10714-012-1452-2

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