Gravitational collapse and Hawking-like radiation of the shell in AdS spacetime

TL;DR

This paper investigates gravitational collapse of a shell in AdS spacetime, deriving equations of motion, analyzing particle radiation spectrum, and exploring unitarity preservation through density matrix off-diagonal elements.

Contribution

It introduces a method to study shell collapse in AdS, computes Hawking-like radiation spectrum, and emphasizes the role of off-diagonal density matrix elements in maintaining unitarity.

Findings

Radiation spectrum matches Hawking results at late times

Reproduces Hawking-Page transition in 3+1 dimensions

Off-diagonal density matrix elements are crucial for unitarity

Abstract

In this paper, we study the collapse of a massive shell in 2+1 and 3+1 dimensional gravity with Anti-de Sitter asymptotics. Using the Gauss-Codazzi method, we derive gravitational equations of motion of the shell. We then use the functional Schrodinger formalism to calculate the spectrum of particles produced during the collapse. At the late time, radiation agrees very well with the standard Hawking results. In 3+1 dimensions, we reproduce the Hawking-Page transition. We then construct the density matrix of this collapsing system and analyze the information content in the emitted radiation. We find that the off-diagonal elements of the density matrix are very important in preserving the unitarity of the system.