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Homothetic motions in general relativity

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Abstract

Properties of homothetic or self-similar motions in general relativity are examined with particular reference to vacuum and perfect-fluid space-times. The role of the homothetic bivector with componentsH [a;b] formed from the homothetic vectorH is discussed in some detail. It is proved that a vacuum space-time only admits a nontrivial homothetic motion if the homothetic vector field is non-null and is not hypersurface orthogonal. As a subcase of a more general result it is shown that a perfect-fluid space-time cannot admit a nontrivial homothetic vector which is orthogonal to the fluid velocity 4-vector.

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  1. Mathematics Department, Monash University, 3168, Clayton, Victoria, Australia

    C. B. G. McIntosh

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  1. C. B. G. McIntosh
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McIntosh, C.B.G. Homothetic motions in general relativity. Gen Relat Gravit 7, 199–213 (1976). https://doi.org/10.1007/BF00763435

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