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Shear-free perfect fluids with a \(\gamma \)-law equation of state

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Abstract

We investigate all shear-free perfect fluid solutions of the Einstein field equations where the pressure and energy density satisfy a \(\gamma \)-law equation of state with \(\mu +p\ne 0\). We prove that such a fluid is either non rotating or non expanding. As a consequence, it follows by combining our result with those of Collins and Wainwright that any such shear-free perfect fluid which models either an expand universe or a collapsing star must in fact be a Friedmann–Robertson–Walker spacetime.

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Notes

  1. A Maple worksheet with most calculations is available from the author.

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Authors and Affiliations

  1. School of Information Technology, Deakin University, Geelong, Australia

    J. Carminati

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  1. J. Carminati
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Correspondence to J. Carminati.

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Carminati, J. Shear-free perfect fluids with a \(\gamma \)-law equation of state. Gen Relativ Gravit 47, 45 (2015). https://doi.org/10.1007/s10714-015-1887-3

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  • DOI: https://doi.org/10.1007/s10714-015-1887-3

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