Polarised black holes in ABJM

Abstract

We numerically construct asymptotically AdS 4 solutions to Einstein-Maxwell-dilaton theory. These have a dipolar electrostatic potential turned on at the conformal boundary S 2 × R t . We find two classes of geometries: AdS soliton solutions that encode the full backreaction of the electric field on the AdS geometry without a horizon, and neutral black holes that are "polarised" by the dipolar potential. For a certain range of the electric field E, we find two distinct branches of the AdS soliton that exist for the same value of E. For the black hole, we find either two or four branches depending on the value of the electric field and horizon temperature. These branches meet at critical values of the electric field and impose a maximum value of E that should be reflected in the dual field theory. For both the soliton and black hole geometries, we study boundary data such as the stress tensor. For the black hole, we also consider horizon observables such as the entropy. At finite temperature, we consider the Gibbs free energy for both phases and determine the phase transition between them. We find that the AdS soliton dominates at low temperature for an electric field up to the maximum value. Using the gauge/gravity duality, we propose that these solutions are dual to deformed ABJM theory and compute the corresponding weak coupling phase diagram.1 In the notation of [3] we set Φ 1 = Φ, Φ 2 = Φ 3 = 0, A = A 1 = −A 2 and A 3 = A 4 = 0.

Testing the weak gravity-cosmic censorship connection

“…We now wish to test whether the solutions we have constructed are unstable to forming a scalar field condensate using the mechanism proposed in [12,13]. In order to do this, we will first search for zero-modes following the same strategy as in [35,36]. A static normalizable mode usually marks the transition between stable and unstable solutions.…”

Creating a traversable wormhole

“…(6.16). The intermediate expressions are too cumbersome to be reproduced here, but follow mutatis mutandis calculations done elsewhere [22,23,24].…”

To go or not to go with the flow: Hawking radiation at strong coupling

“…There are many other circumstances where one cannot show that ξ is necessarily zero on solutions of (2.5) (see for instance [36][37][38][39][40]). However, in many of these cases, one can show that the resulting system of equations is Elliptic, and as such one can trust local uniqueness of solutions to determine whether ξ vanishes or not.…”