Semiclassical Collapse of a Sphere of Dust and Hawking Radiation

TL;DR

This paper develops a quantum model of a collapsing dust sphere, deriving conditions for semiclassical approximations, and shows that near the horizon, the quantum field behaves thermally at Hawking temperature, supporting black hole radiation theory.

Contribution

It introduces a canonical quantization of a dust sphere's dynamics and analyzes the conditions for semiclassical validity, linking quantum collapse to Hawking radiation phenomena.

Findings

Quantum equations for dust and gravity are derived.

Semiclassical approximation validity conditions are established.

Near the horizon, the quantum field exhibits thermal behavior at Hawking temperature.

Abstract

The independent dynamical variables of a collapsing homogeneous sphere of dust are 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. On neglecting back-reaction effects, it is also 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.