Backreaction of scalar waves on black holes at low frequencies

TL;DR

This paper analytically examines how low-frequency scalar waves influence Schwarzschild black holes, quantifying the mass increase due to scalar wave backreaction using perturbative methods.

Contribution

It provides a novel analytical calculation of black hole backreaction from scalar waves at low frequencies, employing matched asymptotic expansions.

Findings

Mass increase due to scalar wave absorption quantified

Analytical model for environmental scalar field backreaction

Applicable to arbitrary wave profiles and incoherent radiation

Abstract

We study the accretion of a Schwarzschild black hole due to spherically symmetric perturbations sourced by a minimally coupled massless scalar field. The backreaction of the black hole to low-frequency ingoing scalar waves is computed analytically as a second-order perturbative effect, using matched asymptotic expansions to relate the behaviour of the scalar field in the vicinity of the horizon and at null infinity. As an application of our results, we compute the mass increase due to (i) ingoing wave packets with an arbitrary profile and (ii) incoherent radiation. Our results could serve as a model for the backreaction of environmental scalar fields on black holes.