Uniqueness Theorem for 5-Dimensional Black Holes with Two Axial Killing Fields
By S. Hollands, S. Yazadjiev. 2007
186 citations recorded by the source corpus.
We show that two stationary, asymptotically flat vacuum black holes in 5 dimensions with two commuting axial symmetries are identical if and only if their masses, angular momenta, and their “interval structures” coincide. We also show that the horizon must be topologically either a 3-sphere, a ring, or a Lens-space. Our argument is a generalization of constructions of Morisawa and Ida (based in turn on key work of Maison) who considered the spherical case, combined with basic arguments concerning the nature of the factor manifold of symmetry orbits.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/af3049f85ad07710d47e222164fe29d06acadf46
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In Astronomy and Astrophysics
- Jorge E Santos
- Ó. J. Dias
- Benson Way
- T. Harmark
- Roberto Emparan
- Maria J Rodriguez
- Harvey Reall
- G. Horowitz
In Nuclear and High Energy Physics
- Jorge E Santos
- Benson Way
- Ó. J. Dias
- T. Harmark
- Roberto Emparan
- Maria J Rodriguez
- Harvey Reall
- G. Horowitz
Citations in the corpus
- Black Holes in Higher Dimensions (2008, background): “It has been proven that these data (whose relation to physical parameters is unfortunately not quite direct), in addition to the total mass and angular momenta, uniquely characterize asymptotically-flat solutions [139].”
- Numerical methods for finding stationary gravitational solutions (2015, background): “On the other hand, the essentials of the rigidity theorem are kept unchanged in its extension to higher dimensions (d > 4) and AdS asymptotics [350, 351] (see also [352–354]).”
- No dynamics in the extremal Kerr throat (2009, methodology): “For technical details, we refer the reader to [27, 28, 30].”
- The Phase Structure of Higher-Dimensional Black Rings and Black Holes (2007, background): “There exist furthermore algebraic classifications of spacetimes [13, 14, 15, 16], and theorems on how to determine uniquely the black hole solutions with two symmetry axes [17, 18].”