Abstract
We study the doubly holographic model of [1] in the situation where a black hole in two-dimensional JT gravity theory is coupled to an auxiliary bath system at arbitrary finite temperature. Depending on the initial temperature of the black hole relative to the bath temperature, the black hole can lose mass by emitting Hawking radiation, stay in equilibrium with the bath or gain mass by absorbing thermal radiation from the bath. In all of these scenarios, a unitary Page curve is obtained by applying the usual prescription for holographic entanglement entropy and identifying the quantum extremal surface for the generalized entropy, using both analytical and numeric calculations. As the application of the entanglement wedge reconstruction, we further investigate the reconstruction of the black hole interior from a subsystem containing the Hawking radiation. We examine the roles of the Hawking radiation and also the purification of the thermal bath in this reconstruction.
Highlights
Background and setupThe AEM4Z model [1] has three holographic descriptions — see figure 1
We study the dynamics of coupling the initial equilibrium black hole to a bath boundary conformal field theory (BCFT) which is initially in a finite non-zero temperature state instead
As in [19], we find that the quantum extremal surfaces can lie outside the black hole horizon, and correspondingly the quantum extremal islands (QEIs) can include part of the exterior of the black hole
Summary
The AEM4Z model [1] has three holographic descriptions — see figure 1. Similar to previous work in the evaporating AdS2 black hole in JT gravity [3], we break the process of calculating the generalized entropy into three steps:. Similar to previous work in the evaporating AdS2 black hole in JT gravity [3], we break the process of calculating the generalized entropy into three steps:4 These steps are very similar to the evaporating models in [1, 3, 20], the only change coming from the details of the time reparametrization function in eq (2.29) and the extra conformal transformation in eq (2.18) required to map the vacuum on upper half plane to our quenched system. We proceed to carry out each one of these steps in the rest of this section
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