Searching for the classical version of Hawking radiation and screening of Coulomb field by the horizon

TL;DR

This paper explores the theoretical possibility of classical Hawking radiation as purely outgoing solutions in a collapsing black hole spacetime, using analytical and numerical methods to analyze scalar field equations.

Contribution

It introduces a novel investigation into classical solutions resembling Hawking radiation, employing a simplified shell collapse model and advanced mathematical techniques.

Findings

Existence of purely outgoing scalar field solutions outside collapsing shells.

Expression of solutions in terms of confluent Heun functions.

Numerical solutions indicating potential classical analogs of Hawking radiation.

Abstract

We investigate the possibility of the existence of a classical version of Hawking radiation - solutions to classical field equations that consist solely of outgoing waves, in the spacetime of a collapsing black hole. The non-static nature of the corresponding metric results in the absence of energy conservation for matter, which could otherwise a priori prohibit such solutions. A specific and simple scenario is considered: a black hole formation as a result of the collapse of a thin shell, which is not necessarily dust-like. In the corresponding spacetime, we study solutions of the equations for a real massless scalar field that take the form of purely outgoing waves. In addition to the homogeneous equation, we also examine the case of a constant point source of the field located at the symmetry center. The general solution outside the shell is expressed in terms of the confluent Heun function, while the equations inside the shell and the matching conditions at its surface are formulated as an integral equation. The analysis of various solution asymptotics enables the reduction of the integral equation to a matrix equation, which is subsequently solved numerically.