Black hole singularities across phase transitions

TL;DR

This paper investigates how black hole singularities behave during phase transitions, revealing that Kasner exponents change continuously or discontinuously depending on the order of the transition, with implications for dual field theories.

Contribution

It uncovers the behavior of Kasner singularities across phase transitions and proposes their potential observables in dual field theories, highlighting universality aspects.

Findings

Kasner exponents are continuous during second order transitions

Kasner exponents are discontinuous during first order transitions

Possible dual field theory observables encode Kasner exponents

Abstract

We study the behavior of black hole singularities across the Hawking-Page phase transitions, uncovering possible connections between the physics inside and outside the horizon. We focus on the case of spacelike singularities in Einstein-scalar theory which are of the Kasner form. We find that the Kasner exponents are continuous and non-differentiable during the second order phase transitions, while discontinuous in the first order phase transitions. We give some arguments on the universality of this behavior. We also discuss possible observables in the dual field theory which encode the Kasner exponents.