2003/09/30 by Sanjeev S. Seahra, Paul S. Wesson · 33 citations
Mathematics · Physics and Astronomy · #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #Black hole (networking) #Constant (computer programming) #Coordinate system #Cosmology and Gravitation Theories #Einstein #Einstein field equations #Equivalence (formal languages) #Field (mathematics) #Geometry #Mathematical physics #Mathematics #Physics #Pure mathematics #Theoretical physics #gr-qc #hep-th
paper · pdf · doi:10.1063/1.1623617
published in Journal of Mathematical Physics 44(12), 5664-5680 (American Institute of Physics) · Reference added, 20 pages, 3 figures, REVTeX4
openalex publication_date 2003/11/22 · arxiv created 2004/01/07 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We clarify the status of two known solutions to the five-dimensional vacuum Einstein field equations derived by Liu, Mashhoon, and Wesson (LMW) and Fukui, Seahra, and Wesson (FSW), respectively. Both 5-metrics explicitly embed four-dimensional Friedman–Lemaı̂tre–Robertson–Walker cosmologies with a wide range of characteristics. We show that both metrics are also equivalent to five-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 five 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.