Consistency of the mass variation formula for black holes accreting cosmological fluids

TL;DR

This paper derives a relativistic formula for black hole mass variation during spherical accretion of cosmological fluids, providing a fundamental basis for existing accretion models and clarifying the conditions under which the formula applies.

Contribution

It introduces a first-principles derivation of the black hole mass variation formula for accreting fluids under specific metric conditions, enhancing theoretical understanding.

Findings

Derived a relativistic mass variation formula for black holes accreting fluids.

Established conditions on the metric for the formula's validity.

Provided a foundational derivation supporting existing accretion models.

Abstract

We address the spherical accretion of generic fluids onto black holes. We show that, if the black hole metric satisfies certain conditions, in the presence of a test fluid it is possible to derive a fully relativistic prescription for the black hole mass variation. Although the resulting equation may seem obvious due to a form of it appearing as a step in the derivation of the Schwarzschild metric, this geometrical argument is necessary to fix the added degree of freedom one gets for allowing the mass to vary with time. This result has applications on cosmological accretion models and provides a derivation from first principles to serve as a base to the accretion equations already in use in the literature.