A rotating hairy AdS<inf>3</inf> black hole with the metric having only one Killing vector field

Norihiro Iizuka, Akihiro Ishibashi, Kengo Maeda

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Abstract: We perturbatively construct a three-dimensional rotating AdS black hole with a real scalar hair. We choose the mass of a scalar field slightly above the Breitenlohner-Freedman bound and impose a general boundary condition for the bulk scalar field at AdS infinity. We first show that rotating BTZ black holes are unstable against scalar field perturbations under our more general boundary condition. Next we construct a rotating hairy black hole perturbatively with respect to a small amplitude ϵ of the scalar field, up to O(ϵ<sup>4</sup>). Our hairy black hole is stationary and exhibits no dissipation, but the lumps of the non-linearly perturbed geometry break axial symmetry, thus providing the first example of a rotating black hole whose metric admits only one Killing vector field. Furthermore, we numerically show that the entropy of our hairy black hole is larger than that of the BTZ black hole with the same energy and the angular momentum. We briefly discuss if our rotating hairy black hole in lumpy geometry could be the endpoint of the instability.

Original languageEnglish
Article number112
JournalJournal of High Energy Physics
Volume2015
Issue number8
DOIs
Publication statusPublished - 2015 Aug 31

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scalars
boundary conditions
hair
geometry
infinity
dissipation
angular momentum
entropy
perturbation
symmetry
energy

Keywords

  • Black Holes
  • Classical Theories of Gravity

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

Cite this

A rotating hairy AdS<inf>3</inf> black hole with the metric having only one Killing vector field. / Iizuka, Norihiro; Ishibashi, Akihiro; Maeda, Kengo.

In: Journal of High Energy Physics, Vol. 2015, No. 8, 112, 31.08.2015.

Research output: Contribution to journalArticle

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N2 - Abstract: We perturbatively construct a three-dimensional rotating AdS black hole with a real scalar hair. We choose the mass of a scalar field slightly above the Breitenlohner-Freedman bound and impose a general boundary condition for the bulk scalar field at AdS infinity. We first show that rotating BTZ black holes are unstable against scalar field perturbations under our more general boundary condition. Next we construct a rotating hairy black hole perturbatively with respect to a small amplitude ϵ of the scalar field, up to O(ϵ4). Our hairy black hole is stationary and exhibits no dissipation, but the lumps of the non-linearly perturbed geometry break axial symmetry, thus providing the first example of a rotating black hole whose metric admits only one Killing vector field. Furthermore, we numerically show that the entropy of our hairy black hole is larger than that of the BTZ black hole with the same energy and the angular momentum. We briefly discuss if our rotating hairy black hole in lumpy geometry could be the endpoint of the instability.

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