Polarised black holes in AdS

Abstract

We consider solutions in Einstein-Maxwell theory with a negative cosmological constant that asymptote to global AdS 4 with conformal boundary S 2 × R t . At the sphere at infinity we turn on a space-dependent electrostatic potential, which does not destroy the asymptotic AdS behaviour. For simplicity we focus on the case of a dipolar electrostatic potential. We find two new geometries: (i) an AdS soliton that includes the full backreaction of the electric field on the AdS geometry; (ii) a polarised neutral black hole that is deformed by the electric field, accumulating opposite charges in each hemisphere. For both geometries we study boundary data such as the charge density and the stress tensor. For the black hole we also study the horizon charge density and area, and further verify a Smarr formula. Then we consider this system at finite temperature and compute the Gibbs free energy for both AdS soliton and black hole phases. The corresponding phase diagram generalizes the Hawking-Page phase transition. The AdS soliton dominates the low temperature phase and the black hole the high temperature phase, with a critical temperature that decreases as the external electric field increases. Finally, we consider the simple case of a free charged scalar field on S 2 × R t with conformal coupling. For a field in the SU (N ) adjoint representation we compare the phase diagram with the above gravitational system. arXiv:1511.08505v1 [hep-th] 26 Nov 2015 ✓ AdS Boundary AdS Soliton ✓ Black Hole

Geometric polarization of plasmas and Love numbers of AdS black branes

“…Consistently with this, observe that if we rescale 17) and also perform a rescaling of z (which makesh zz = 0), then we can makeh tt disappear from (3.15). In other words, the apparent spatial dependence of the plasma temperature does not have any invariant meaning for a CFT.…”

“…But it is also possible and interesting to study the electric and gravitational polarization of black holes in global AdS -in dual terms, the polarization of the plasma on a spherical space. Indeed, the fully non-linear effects of electric polarization for these black holes have been studied numerically already in [17,18], see also [19][20][21]. The analysis in global AdS is technically more complicated (spherical harmonics instead of plane waves) and presumably less relevant to systems in the lab, so we have not attempted it here.…”

Maxwell perturbations on Kerr–anti–de Sitter black holes: Quasinormal modes, superradiant instabilities, and vector clouds

“…It will then be interesting to understand the interplay between this well known family and the new family of "hairy" BHs. A different family of static BHs, in the Einstein-MaxwellAdS system, was reported in [50] (see also [9,51]). asymptotically, one concludes that there are no contributions for the angular momentum flux from the first term T r φ;I .…”

Static Einstein-Maxwell Black Holes with No Spatial Isometries in AdS Space

“…A static, axially symmetric BH within a dipole soliton was constructed in Ref. [32]. Here, we construct static BHs without any spatial isometry, which, as we shall see, require solitons with higher multipoles.…”

“…[31] by simple considerations of electrostatics in global AdS; fully noninearly examples were presented in Refs. [32] and [33]. In a nutshell, we note the following.…”