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

Abstract

In this paper, we study the collapse of a massive shell in 2 þ 1 and 3 þ 1 dimensional gravity with antide Sitter asymptotics. Using the Gauss-Codazzi method, we derive gravitational equations of motion of the shell. We then use the functional Schrödinger 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 þ 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 offdiagonal elements of the density matrix are very important in preserving the unitarity of the system.

Formation of the Hayward black hole from a collapsing shell

“…[19], the density matrix of the quantum radiation was also calculated explicitly, which shows that the process of the radiation is unitary during the evolution [20,21]. This fact was confirmed in the other singular black holes such as the anti-de Sitter Schwarzschild black hole and the Reissner-Nordström black hole [22,23]. Now, one might wonder how this collapsing process including the functional Schrodinger method works in the Hayward black hole as a regular black hole.…”

“…because ζ(η) is real regardless of H. Therefore, the process of radiation turns out to be unitary during the evolution in the Hayward black hole, which is similar to the evolution process of singular black holes [20][21][22][23]. This fact can also be understood from the conservation law of a probability current.…”

“…The spacetime will be divided into the interior and the exterior regions of an infinitely thin shell with a radius R(t) [13][14][15][16][17][18][20][21][22][23]. In the exterior region of the shell, i.e., r > R(t), the spacetime is described by the Hayward metric [4] (ds…”

Unitarity in Reissner–Nordström background: striding away from information loss

“…We compute the density matrices,ρ i andρ f , for the initial (J − ) and the final (J + ) states respectively. We can write theρ i andρ f as (see [10,11]),…”

Unitary black hole radiation: Schwarzschild-global monopole background

“…We shall now calculate the density matrices,ρ i and ρ f , for the initial (J − ) and the final (J + ) states respec-tively.ρ i andρ f can be written as (see [12,13]),…”