The Method of Comparison Equations for Schwarzschild Black Holes

TL;DR

This paper applies the method of comparison equations to analyze scalar field propagation around Schwarzschild black holes, providing accurate approximate solutions relevant for black hole evaporation studies.

Contribution

It introduces the use of comparison equations for deriving explicit approximate radial modes in Schwarzschild spacetime, improving solution accuracy for energies below the potential peak.

Findings

Explicit approximate radial modes obtained

High accuracy outside the horizon

Potential applications to black hole evaporation

Abstract

We employ the method of comparison equations to study the propagation of a massless minimally coupled scalar field on the Schwarzschild background. In particular, we show that this method allows us to obtain explicit approximate expressions for the radial modes with energy below the peak of the effective potential which are fairly accurate over the whole region outside the horizon. This case can be of particular interest, for example, for the problem of black hole evaporation.