Backreaction of accreting matter onto a black hole in the Eddington-Finkelstein coordinates

TL;DR

This paper investigates how accreting matter affects the spacetime geometry of a black hole using perturbation theory in Eddington-Finkelstein coordinates, revealing that near the horizon, corrections resemble the Vaidya solution.

Contribution

It provides general expressions for metric corrections due to accretion in Eddington-Finkelstein coordinates and links these to the Vaidya solution near the horizon.

Findings

Leading metric corrections near the horizon are of the Vaidya form.

Derived general expressions for metric perturbations due to accretion.

Discussed relations to other known solutions and provided specific examples.

Abstract

We study backreaction of accreting matter onto a spherically symmetric black hole in a perturbative way, when accretion is in a quasi-steady state. General expressions for corrections to the metric coefficients are found in the Eddington-Finkelstein coordinates. It is shown that near the horizon of a black hole, independently of the form of the energy-momentum tensor, the leading corrections to the metric are of the Vaidya form. The relation to other solutions is discussed and particular examples are presented.