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.
Highlights
Where τ is a function of radial coordinate and the Kasner exponents pt, pi, pφ satisfy pt +
The black hole singularities are located behind the horizon of the black holes, their information could can be extracted from the physical quantities of the dual field theory in the context of AdS/CFT correspondence, e.g. correlation functions [16,17,18], entanglement entropies [19] etc
We have studied the behaviors of the singularities in Einstein-scalar theory with a double trace deformation in which the second order and the first order phase transitions could be realized
Summary
We begin by collecting all the necessary ingredients for constructing black hole solutions and studying the phase transitions in a four dimensional Einstein scalar theory in AdS. We will first present the four dimensional Einstein-scalar theory under consideration and show the numerical strategy to solve the system from the boundary to the singularity. We will study the thermodynamics of the black hole solutions in order to study the phase diagrams of the system from which the singularity behavior could be uncovered
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