Quantum radiation of a collapsing shell in three-dimensional AdS spacetime revisited

TL;DR

This paper investigates quantum radiation during gravitational collapse in three-dimensional AdS space, showing that the radiation temperature matches Hawking temperature regardless of interior geometry choices.

Contribution

It provides an exact wave function solution for a massless scalar field during collapse and derives analytic expressions for occupation numbers and radiation temperature.

Findings

Radiation temperature agrees with Hawking temperature

Exact wave function obtained for massless scalar field

Occupation number expressions derived analytically

Abstract

In three-dimensional AdS space, we consider the gravitational collapse of dust shell and then investigate the quantum radiation from the collapsing shell by employing the functional Schr\"odinger formalism. In the formation of the BTZ black hole, the interior geometry of the shell can be chosen as either the massless black hole or the global AdS space. In the incipient black hole limit, we obtain the wave function exactly from the time-dependent Schr\"odinger equation for a massless scalar field. Then, we show that the occupation number of excited states can be written by analytic expressions, and the radiation temperature is in agreement with the Hawking temperature, irrespective of the specific choice of the interior geometries.