Semiclassical collapse of a sphere of dust

TL;DR

This paper investigates the quantum aspects of a collapsing dust sphere, deriving conditions for approximations and showing that near the horizon, the scalar field behaves thermally at Hawking temperature.

Contribution

It provides a canonical quantization framework for dust collapse and analyzes the thermal nature of scalar fields near the horizon without back-reaction effects.

Findings

Wightman function is thermal near the horizon

Conditions for adiabatic and semiclassical approximations are established

Back-reaction effects are neglected in the analysis

Abstract

The semiclassical collapse of a homogeneous sphere of dust is studied. After identifying the independent dynamical variables, the system is canonically quantised and coupled equations describing matter (dust) and gravitation are obtained. The conditions for the validity of the adiabatic (Born--Oppenheimer) and semiclassical approximations are derived. Further on neglecting back--reaction effects, it is shown that in the vicinity of the horizon and inside the dust the Wightman function for a conformal scalar field coupled to a monopole emitter is thermal at the characteristic Hawking temperature.