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Universes encircling 5-dimensional black holes

Sanjeev S. Seahra·Paul S. Wesson
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Abstract

We clarify the status of two known solutions to the 5-dimensional vacuum Einstein field equations derived by Liu, Mashhoon & Wesson (LMW) and Fukui, Seahra & Wesson (FSW), respectively. Both 5-metrics explicitly embed 4-dimensional Friedman-Lemaitre-Robertson-Walker cosmologies with a wide range of characteristics. We show that both metrics are also equivalent to 5-dimensional topological black hole (TBH) solutions, which is demonstrated by finding explicit coordinate transformations from the TBH to LMW and FSW line elements. We argue that the equivalence is a direct consequence of Birkhoff's theorem generalized to 5 dimensions. Finally, for a special choice of parameters we plot constant coordinate surfaces of the LMW patch in a Penrose-Carter diagram. This shows that the LMW coordinates are regular across the black and/or white hole horizons.

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Sanjeev S. Seahra, Paul S. Wesson. 2004-01-07. Universes encircling 5-dimensional black holes. https://doi.org/10.1063/1.1623617

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