Lumpy AdS5× S5 black holes and black belts

Abstract

Sufficiently small Schwarzschild black holes in global AdS 5 ×S 5 are GregoryLaflamme unstable. We construct new families of black hole solutions that bifurcate from the onset of this instability and break the full SO(6) symmetry group of the S 5 down to SO(5). These new "lumpy" solutions are labelled by the harmonics . We find evidence that the = 1 branch never dominates the microcanonical/canonical ensembles and connects through a topology-changing merger to a localised black hole solution with S 8 topology. We argue that these S 8 black holes should become the dominant phase in the microcanonical ensemble for small enough energies, and that the transition to Schwarzschild black holes is first order. Furthermore, we find two branches of solutions with = 2. We expect one of these branches to connect to a solution containing two localised black holes, while the other branch connects to a black hole solution with horizon topology S 4 × S 4 which we call a "black belt".

Hairy black holes in AdS5 × S 5

“…For instance, small Schwarzschild-AdS black holes can be shown to be unstable to a localisation on the S 5 if their radius in AdS units is sufficiently small [5][6][7][8]. The bumpy black holes in AdS 5 × S 5 that branch from the onset of this instability were only recently constructed and necessarily require solving partial differential equations [9]. The work developed in this paper ignores such instabilities and focuses on solutions of fivedimensional N = 8 gauged supergravity, which is thought to be a consistent truncation of IIB supergravity on AdS 5 × S 5 .…”

LocalizedAdS5×S5Black Holes

“…The existence of a symmetry-breaking phase transition can be inferred from a Gregory-Laflamme instability whereby small AdS 5 -Schwarzschild×S 5 (AdSSchw 5 × S 5 ) black holes [5,6] become unstable to deformations of the S 5 due to a separation of horizon length scales [7][8][9][10][11][12][13][14]. However, only recently has it been found that the phase transition is first order [12].…”

“…However, only recently has it been found that the phase transition is first order [12]. The location of the phase transition and the expectation value of the scalar operators remain unknown.…”

“…We use the DeTurck method [15,16] (see [14] for a review). The method requires the choice of a reference metric g from which one obtains the DeTurck vector…”

Universality of small black hole instability in AdS/CFT

“…It is expected that an AdS 5 black hole can not become arbitrarily small: it was proposed in [6,7] that in the limit ρ + → 0 it would suffer a Gregory-Laflamme (GL) instability [8], resulting in its localization on V 5 . The latter localization phenomenon was explicitly verified in [5,9,10] Holographic dual to thermal states of a large class of conformal gauge theories on R × S 3 is described by the following type IIb supergravity background…”