Effect of Scalar Mass in the Absorption and Emission Spectra of Schwarzschild Black Hole

TL;DR

This paper studies how scalar mass influences the absorption and emission spectra of 4D Schwarzschild black holes, revealing that mass breaks universality in low-energy cross sections and reduces emission rates.

Contribution

It provides a numerical analysis of scalar mass effects on black hole spectra, extending previous massless studies with new insights into low-energy behavior and emission suppression.

Findings

Scalar mass decreases low-energy S-wave absorption cross section.

Massive scalars break the universality of low-energy cross section equals horizon area.

Scalar mass generally reduces Hawking emission rates.

Abstract

Following Sanchez's approach we investigate the effect of scalar mass in the absorption and emission problems of 4d Schwarzschild black hole. The absorption cross sections for arbitrary angular momentum of the scalar field are computed numerically in the full range of energy by making use of the analytic near-horizon and asymptotic solutions and their analytic continuations. The scalar mass makes an interesting effect in the low-energy absorption cross section for S-wave. Unlike the massless case, the cross section decreases with increasing energy in the extremely low-energy regime. As a result the universality, {\it i.e.} low-energy cross section for S-wave is equal to the horizon area, is broken in the presence of mass. If the scalar mass is larger than a critical mass, the absorption cross section becomes monotonically decreasing function in the entire range of energy. The Hawking emission is also calculated numerically. It turns out that the Planck factor generally suppresses the contribution of higher partial waves except S-wave. The scalar mass in general tends to reduce the emission rate.