### 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 language | English |
---|---|

Article number | 112 |

Journal | Journal of High Energy Physics |

Volume | 2015 |

Issue number | 8 |

DOIs | |

Publication status | Published - 2015 Aug 31 |

### Fingerprint

### Keywords

- Black Holes
- Classical Theories of Gravity

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*,

*2015*(8), [112]. https://doi.org/10.1007/JHEP08(2015)112

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

Research output: Contribution to journal › Article

*Journal of High Energy Physics*, vol. 2015, no. 8, 112. https://doi.org/10.1007/JHEP08(2015)112

}

TY - JOUR

T1 - A rotating hairy AdS3 black hole with the metric having only one Killing vector field

AU - Iizuka, Norihiro

AU - Ishibashi, Akihiro

AU - Maeda, Kengo

PY - 2015/8/31

Y1 - 2015/8/31

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.

AB - 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.

KW - Black Holes

KW - Classical Theories of Gravity

UR - http://www.scopus.com/inward/record.url?scp=84940565994&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84940565994&partnerID=8YFLogxK

U2 - 10.1007/JHEP08(2015)112

DO - 10.1007/JHEP08(2015)112

M3 - Article

VL - 2015

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 8

M1 - 112

ER -