Critical lumpy black holes in AdSp×Sq

Abstract

In this paper we study lumpy black holes with AdSp × Sq asymptotics, where the isometry group coming from the sphere factor is broken down to SO(q). Depending on the values of p and q, these are solutions to a certain Supergravity theory with a particular gauge field. We have considered the values (p, q) = (5, 5) and (p, q) = (4, 7), corresponding to type IIB supergravity in ten dimensions and eleven-dimensional supergravity respectively. These theories presumably contain an infinite spectrum of families of lumpy black holes, labeled by a harmonic number ℓ, whose endpoints in solution space merge with another type of black holes with different horizon topology. We have numerically constructed the first four families of lumpy solutions, corresponding to ℓ = 1, 2+, 2− and 3. We show that the geometry of the horizon near the merger is well-described by a cone over a triple product of spheres, thus extending Kol’s local model to the present asymptotics. Interestingly, the presence of non-trivial fluxes in the internal sphere implies that the cone is no longer Ricci flat. This conical manifold accounts for the geometry and the behavior of the physical quantities of the solutions sufficiently close to the critical point. Additionally, we show that the vacuum expectation values of the dual scalar operators approach their critical values with a power law whose exponents are dictated by the local cone geometry in the bulk.

Gregory-Laflamme and superradiance encounter black resonator strings

“…They produce a plethora of physical phenomena not found in four-dimensional gravity, including the Gregory-Laflamme instability [2,3], non-uniqueness [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19], and violations of the weak cosmic censorship [20,21]. The same physics is found in other higher dimensional black holes, including black rings [22][23][24], ultraspinning black holes [25][26][27][28][29][30][31][32][33], and certain black holes in supergravity [34][35][36][37][38][39][40].…”

Stability of the microcanonical ensemble in Euclidean Quantum Gravity

“…One such example occurs when we consider embedding the Euclidean Schwarzschild-AdS 5 in IIB supergravity with AdS 5 Ŝ5 asymptotics via the standard Freud-Rubin compactifications [37]. At small energies the usual Schwarzschild-AdS 5 black hole becomes dynamically unstable [4,[38][39][40][41][42][43][44][45] to the Gregory-Laflamme instability [46]. The endpoint of this instability has been argued to be a ten-dimensional localised black hole, which has been constructed in [44] and also admits a regular Euclidean section.…”

New phases of $$ \mathcal{N} $$ = 4 SYM at finite chemical potential

“…We now consider a restriction of (2.1) which preserves a Z denotes a rotation by π in the complex z K plane (under which z K , zK Ñ ´zK , ´z K ). 10 In detail, matching the low energy limit of string theory with type IIB supergravity in the Einstein frame one finds that the 10-dimensional Newton constant is G10 " 8π 6 g 2 s 8 s where gs and s are the string coupling and string length respectively. The t'Hooft coupling is λ " g 2 YM N where for p-branes the YM coupling is given by g 2 YM " p2πq p´2 gs p´3 s .…”

“…ˆS5 but break the SOp6q symmetry of S 5 down to SOp5q have also been found recently. They describe either lumpy black holes with polar deformations along the S 5 [9,10] or black holes that localize on the S 5 [11] (the latter have S 8 horizon topology). Their existence demonstrates how important it is to find the full phase diagram of asymptotically global AdS 5 ˆS5 black holes.…”