Black holes and the absorption rate of cosmological scalar fields

TL;DR

This paper investigates how a massless scalar field is absorbed by a static black hole, revealing that absorption depends on wave characteristics and establishing a minimum absorption fraction of about 50%.

Contribution

It introduces a normalized absorption rate based on the Klein-Gordon equation and analyzes its dependence on wave properties, providing new insights into scalar field-black hole interactions.

Findings

Absorption rate depends on wavelength and wave packet width.

Absorption is insensitive to scalar field strength.

Minimum absorption fraction is approximately 50%.

Abstract

We study the absorption of a massless scalar field by a static black hole. Using the continuity equation that arises from the Klein-Gordon equation, it is possible to define a normalized absorption rate $\Gamma(t)$ for the scalar field as it falls into the black hole. It is found that the absorption mainly depends upon the characteristics wavelengths involved in the physical system: the mean wavenumber and the width of the wave packet, but that it is insensitive to the scalar field's strength. By taking a limiting procedure, we determine the minimum absorption fraction of the scalar field's mass by the black hole, which is around 50%.