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

N1 - Publisher Copyright:
© 2015, The Author(s).

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

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U2 - 10.1007/JHEP08(2015)112

DO - 10.1007/JHEP08(2015)112

M3 - Article

AN - SCOPUS:84940565994

SN - 1126-6708

VL - 2015

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 8

M1 - 112

ER -