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Time dependent black holes and thermal equilibration

Dongsu Bak, Michael Gutperle, Andreas Karch

TL;DR

The paper analyzes exact time-dependent black hole solutions in AdS/CFT to model thermalization in a strongly coupled gauge theory. By constructing a thermofield state from the Euclidean continuation and matching field theory correlators to gravity, it shows the non-conserved Lagrangian density relaxes exponentially with a calculable thermalization time, while the energy-momentum tensor remains at its equilibrium form to leading order in the deformation. The results demonstrate coherent gravity-field theory duality during non-equilibrium evolution and discuss how unitarity is recovered nonperturbatively in the planar limit. The work provides a controlled holographic platform to study equilibration and clarifies the role of Poincaré recurrence and possible instabilities in time-dependent AdS spacetimes.

Abstract

We study aspects of a recently proposed exact time dependent black hole solution of IIB string theory using the AdS/CFT correspondence. The dual field theory is a thermal system in which initially a vacuum density for a non-conserved operator is turned on. We can see that in agreement with general thermal field theory expectation the system equilibrates: the expectation value of the non-conserved operator goes to zero exponentially and the entropy increases. In the field theory the process can be described quantitatively in terms of a thermofield state and exact agreement with the gravity answers is found.

Time dependent black holes and thermal equilibration

TL;DR

The paper analyzes exact time-dependent black hole solutions in AdS/CFT to model thermalization in a strongly coupled gauge theory. By constructing a thermofield state from the Euclidean continuation and matching field theory correlators to gravity, it shows the non-conserved Lagrangian density relaxes exponentially with a calculable thermalization time, while the energy-momentum tensor remains at its equilibrium form to leading order in the deformation. The results demonstrate coherent gravity-field theory duality during non-equilibrium evolution and discuss how unitarity is recovered nonperturbatively in the planar limit. The work provides a controlled holographic platform to study equilibration and clarifies the role of Poincaré recurrence and possible instabilities in time-dependent AdS spacetimes.

Abstract

We study aspects of a recently proposed exact time dependent black hole solution of IIB string theory using the AdS/CFT correspondence. The dual field theory is a thermal system in which initially a vacuum density for a non-conserved operator is turned on. We can see that in agreement with general thermal field theory expectation the system equilibrates: the expectation value of the non-conserved operator goes to zero exponentially and the entropy increases. In the field theory the process can be described quantitatively in terms of a thermofield state and exact agreement with the gravity answers is found.

Paper Structure

This paper contains 6 sections, 44 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Time dependent black holes
  3. Correspondence
  4. Construction of the thermofield state
  5. Check for the thermofield state
  6. Discussion

Figures (2)

  • Figure 1: Penrose diagram for the time dependent black hole. The $\tau$ ($\in [-\pi/2,\pi/2]$) coordinate runs vertically upward and $\mu$ ($\in [-\mu_0,\mu_0]$) to the right horizontally.
  • Figure 2: The conformal diagram of the Euclidean solution in ($\mu$, $\tau_E$) space. The curves represent constant $\mu$ lines. Along the curves, $\tau_E$ runs from $-\infty$ at $B$ to $+\infty$ at $A$ in the upward direction. The right (left) half of boundary corresponds to $\mu= \mu_0$ ($\mu=-\mu_0$). The dotted line is the $\tau_E =0$ line and the lower half is used to construct the thermofield state.