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Generalized Weyl solutions
Open accessAbstract
It was shown by Weyl that the general static axisymmetric solution of the vacuum Einstein equations in four dimensions is given in terms of a single axisymmetric solution of the Laplace equation in three-dimensional flat space. Weyl's construction is generalized here to arbitrary dimension $D>~4.$ The general solution of the D-dimensional vacuum Einstein equations that admits $D\ensuremath{-}2$ orthogonal commuting non-null Killing vector fields is given either in terms of $D\ensuremath{-}3$ independent axisymmetric solutions of Laplace's equation in three-dimensional flat space or by $D\ensuremath{-}4$ independent solutions of Laplace's equation in two-dimensional flat space. Explicit examples of new solutions are given. These include a five-dimensional asymptotically flat ``black ring'' with an event horizon of topology ${S}^{1}\ifmmode\times\else\texttimes\fi{}{S}^{2}$ held in equilibrium by a conical singularity in the form of a disk.
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Cites
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A Rotating Black Ring Solution in Five Dimensions
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Cited by
Static axisymmetric vacuum solutions and non-uniform black strings
Wiseman, T. (2003) · Classical and Quantum Gravity · doi:10.1088/0264-9381/20/6/308 · Cited by 254
Small localized black holes in a braneworld: Formulation and numerical method
Kudoh, H., Tanaka, T., & Nakamura, T. (2003) · Physical Review D · doi:10.1103/physrevd.68.024035 · Cited by 103
On the existence and dynamics of braneworld black holes
Fitzpatrick, A. L., Randall, L., & Wiseman, T. (2006) · Journal of High Energy Physics · doi:10.1088/1126-6708/2006/11/033 · Cited by 53
Bubbles unbound: bubbles of nothing without Kaluza-Klein
Copsey, K. (2007) · Journal of High Energy Physics · doi:10.1088/1126-6708/2007/12/007 · Cited by 9
New class of accelerating black hole solutions
Camps, J., & Emparan, R. (2010) · Physical Review D · doi:10.1103/physrevd.82.024009 · Cited by 6
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Metadata
- Authors
- Emparan, R., & Reall, H. S.
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2002-04-03
- Volume
- 65
- Issue
- 8
- ISSN
- 0556-2821 (ISSN-L)
- 1089-4918
- OpenAlex
- W2169776339
- Cited by
- 294
- References
- 50
- FWCI
- 9.74
- Type
- journal article
- Language
- en
- Open access
- bronze
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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