Page Curve of AdS-Vaidya Model for Evaporating Black Holes

TL;DR

This paper investigates the entanglement entropy and Page curve of an evaporating black hole in a time-dependent AdS-Vaidya spacetime using holographic methods, introducing a novel moving brane and surface.

Contribution

It presents a new model with a time-dependent brane and surface to study black hole evaporation and entanglement entropy in a dynamic holographic setting.

Findings

Derived a time-dependent Page curve for evaporating black holes.

Introduced the METR brane as a novel element in holographic models.

Analyzed the island formation and entanglement entropy evolution.

Abstract

We study an evaporating black hole in the boundary conformal field theory (BCFT) model under the fully time-dependent AdS-Vaidya spacetime geometry. We introduce the time-dependent finite bath termed the effective Hawking radiation region. This is described by a nontrivial BCFT solution that acts as a time-dependent brane which we call the moving end-of-the-radiation (METR) brane that leads to a new type of Hubeny-Rangamani-Takayanagi surface. We further examine the island formulation in this particular time-dependent spacetime. The Page curve is calculated by using Holographic Entanglement Entropy (HEE) in the context of double holography.