Gravitational duals to the grand canonical ensemble abhor Cauchy horizons

TL;DR

This paper investigates how deformations in the dual conformal field theory influence the internal structure of charged black holes, showing that such deformations typically eliminate Cauchy horizons and lead to Kasner singularities, with implications for holographic duality.

Contribution

It demonstrates that generic scalar deformations remove Cauchy horizons in charged black holes, replacing them with Kasner singularities, and explores the conditions under which horizons can still form.

Findings

Deformations generally eliminate Cauchy horizons in charged black holes.

Relevant deformations prevent the formation of Cauchy horizons.

Irrelevant deformations can allow Cauchy horizons at specific temperatures.

Abstract

The gravitational dual to the grand canonical ensemble of a large $N$ holographic theory is a charged black hole. These spacetimes -- for example Reissner-Nordstr\"om-AdS -- can have Cauchy horizons that render the classical gravitational dynamics of the black hole interior incomplete. We show that a (spatially uniform) deformation of the CFT by a neutral scalar operator generically leads to a black hole with no inner horizon. There is instead a spacelike Kasner singularity in the interior. For relevant deformations, Cauchy horizons never form. For certain irrelevant deformations, Cauchy horizons can exist at one specific temperature. We show that the scalar field triggers a rapid collapse of the Einstein-Rosen bridge at the would-be Cauchy horizon. Finally, we make some observations on the interior of charged dilatonic black holes where the Kasner exponent at the singularity exhibits an attractor mechanism in the low temperature limit.