Plumbing constructions and the domain of outer communication for 5-dimensional stationary black holes
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- by Marcus Khuri, Yukio Matsumoto, Gilbert Weinstein and Sumio Yamada PDF
- Trans. Amer. Math. Soc. 372 (2019), 3237-3256 Request permission
Abstract:
The topology of the domain of outer communication for 5-dimensional stationary bi-axisymmetric black holes is classified in terms of disc bundles over the 2-sphere and plumbing constructions. In particular we find an algorithmic bijective correspondence between the plumbing of disc bundles and the rod structure formalism for such spacetimes. Furthermore, we describe a canonical fill-in for the black hole region and cap for the asymptotic region. The resulting compactified domain of outer communication is then shown to be homeomorphic to $S^4$, a connected sum of $S^2\times S^2$’s, or a connected sum of complex projective planes $\mathbb {CP}^2$. Combined with recent existence results, it is shown that all such topological types are realized by vacuum solutions. In addition, our methods treat all possible types of asymptotic ends, including spacetimes which are asymptotically flat, asymptotically Kaluza-Klein, or asymptotically locally Euclidean.References
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Additional Information
- Marcus Khuri
- Affiliation: Department of Mathematics, Stony Brook University, Stony Brook, New York 11794
- MR Author ID: 811767
- Email: khuri@math.sunysb.edu
- Yukio Matsumoto
- Affiliation: Department of Mathematics, Gakushuin University, Tokyo 171-8588, Japan
- MR Author ID: 202365
- Email: yukiomat@math.gakushuin.ac.jp
- Gilbert Weinstein
- Affiliation: Department of Physics and Department of Mathematics, Ariel University, Ariel, 40700, Israel
- MR Author ID: 293250
- Email: gilbertw@ariel.ac.il
- Sumio Yamada
- Affiliation: Department of Mathematics, Gakushuin University, Tokyo 171-8588, Japan
- MR Author ID: 641808
- Email: yamada@math.gakushuin.ac.jp
- Received by editor(s): July 13, 2018
- Published electronically: May 30, 2019
- Additional Notes: The first author acknowledges the support of NSF Grant DMS-1708798.
The fourth author acknowledges the support of JSPS Grants KAKENHI 24340009 and 17H01091. - © Copyright 2019 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 372 (2019), 3237-3256
- MSC (2010): Primary 53C80, 83C57
- DOI: https://doi.org/10.1090/tran/7812
- MathSciNet review: 3988609