Black hole singularities across phase transitions

Abstract

We study the behavior of black hole singularities across the Hawking-Page phase transitions, uncovering the possible connection 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.

Trans-IR Flows to Black Hole Singularities

“…A natural extension of our work is to consider more types of flows, such as those sourced by combinations of interacting scalars, higher-rank fields, and axions [36][37][38][39][40]72]. One may also consider higher-curvature gravity [52], but note that we would expect corrections to the a T -function by analogy to the a-function of [9,10].…”