Universes encircling fivedimensional black holes
Abstract
We clarify the status of two known solutions to the fivedimensional vacuum Einstein field equations derived by Liu, Mashhoon, and Wesson (LMW) and Fukui, Seahra, and Wesson (FSW), respectively. Both 5metrics explicitly embed fourdimensional FriedmanLemaîtreRobertsonWalker cosmologies with a wide range of characteristics. We show that both metrics are also equivalent to fivedimensional 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 five dimensions. Finally, for a special choice of parameters we plot constant coordinate surfaces of the LMW patch in a PenroseCarter diagram. This shows that the LMW coordinates are regular across the black and/or white hole horizons.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 December 2003
 DOI:
 10.1063/1.1623617
 arXiv:
 arXiv:grqc/0309006
 Bibcode:
 2003JMP....44.5664S
 Keywords:

 04.70.Bw;
 04.20.Jb;
 04.20.Gz;
 02.40.k;
 Classical black holes;
 Exact solutions;
 Spacetime topology causal structure spinor structure;
 Geometry differential geometry and topology;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 Reference added, 20 pages, 3 figures, REVTeX4