Cosmic Censorship at Large D: Stability analysis in polarized AdS black branes (holes)

TL;DR

This paper investigates the stability of polarized AdS black branes and holes at large dimensions, providing new effective equations and arguing that certain instabilities do not violate cosmic censorship.

Contribution

It derives effective equations for polarized AdS black branes and holes at large D, analyzing their stability and supporting cosmic censorship.

Findings

Mushroom-type static solutions with a neck connecting horizons.

Neck cannot be dynamically pinched off due to thermodynamical stability.

Black holes' equatorial plane cannot be sufficiently squashed unless positive specific heat.

Abstract

We test the cosmic censorship conjecture for a class of polarized AdS black branes (holes) in the Einstein-Maxwell theory at large number of dimensions $D$. We first derive a new set of effective equations describing the dynamics of the polarized black branes (holes) to leading order in the $1/D$ expansion. In the case of black branes, we construct `mushroom-type' static solutions from the effective equations, where a spherical horizon is connected with an asymptotic planar horizon through a `neck' which is locally black-string shape. We argue that this neck part (of black string) cannot be pinched off dynamically from the perspective of thermodynamical stability. In the case of black holes, we show that the equatorial plane on the spherical horizon cannot be sufficiently squashed unless the specific heat is positive. We also discuss that the solutions are stable against linear perturbation, agreeing with the thermodynamical argument. These results suggest that Gregory-Laflamme type instability does not occur at the neck, in favor of the cosmic censorship.