Uniqueness and non-uniqueness of static vacuum black holes in higher dimensions

By G. W. Gibbons, D. Ida, T. Shiromizu. 2002

157 citations recorded by the source corpus.

We prove a uniqueness theorem for asymptotically flat static charged dilaton black hole solutions in higher dimensional space-times. We also construct infinitely many non-asymptotically flat regular static black holes on the same space-time manifold with the same spherical topology. An application to the uniqueness of a certain class of flat $p$-branes is also given.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/4f0052626331b2ee639ef8a9c68970eda0b0d19e

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In Applied Mathematics

In Astronomy and Astrophysics

In Nuclear and High Energy Physics

Citations in the corpus

Topology change in general relativity, and the black-hole black-string transition (2002, background): “New localized solutions in decompactified 5d, on the other hand, are forbidden by a generalization of the uniqueness theorem [24, 25 ].”
Black Saturn (2007, background): “The existence of the J = 0 black saturn solutions does not contradict the uniqueness theorem [12] that the Schwarzschild black hole is the only static asymptotically flat vacuum black hole solution; the reason is simply that black saturn, while being stationary, is non-static.”
Uniqueness Theorem for 5-Dimensional Black Holes with Two Axial Killing Fields (2007, background): “In case (i), one can prove that the spacetime is actually uniq ue, and in fact isometric to the Schwarzschild spacetime [22] when n = 4, for higher dimensions see [ 12 ].”
Black Holes in Higher Dimensions (2008, background): “d > 4-dimensions to establish uniqueness of the d > 4-dimensional Schwarzschild solution amongst static vacuum solutions [110].”
A Gravitational instability in higher dimensions (2002, background): “stable spacetimes are given in §5. The vacuum solution for fis of course (21) which is now just the SchwarzschildTangherlini [13] black hole and the Asymptotically Conical (AC) variants considered in [5, 6]. The radial function is f(r) = 1 − α r d−1 . (35) The higher dimensional Regge-Wheeler tortoi”
A new approach to static numerical relativity and its application to Kaluza–Klein black holes (2009, background): “For asymptotically flat D-dimensional gravity in the absence of matter, with D > 4, static black holes are given uniquely by the Schwarzschild–Tangherlini black hole [6–8].”