Universes encircling 5-dimensional black holes

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.

arXiv commentReference added, 20 pages, 3 figures, REVTeX4

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• Naked shell singularities on the brane
• An expanding 4D universe in a 5D Kaluza-Klein cosmology with higher dimensional matter
• Reconstruction of $5D$ Cosmological Models From Equation of State of Dark Energy
• Using (4+1) split and energy conditions to study the induced matter in 5D Ricc-flat cosmology
• The Big Bang as a Phase Transition
• On the validity of the 5-dimensional Birkhoff theorem: The tale of an exceptional case
• Reconstruction of Five-dimensional Bounce cosmological Models From Deceleration Factor
• The primordial explosion of a false white hole from a 5D vacuum
• A five-dimensional vacuum-defect wormhole space-time
• Higher-dimensional topologically charged traversable defect wormhole with non-exotic matter
• Correspondence between modified gravity and 5D Ricci-flat cosmologies
• Exact solutions of embedding the four-dimensional perfect fluid in a five- or higher-dimensional Einstein spacetime and the cosmological interpretations
• Cosmological solutions in the brane-bulk system