Analytical solutions of accreting black holes immersed in a Lambda-CDM model

TL;DR

This paper derives exact analytical solutions describing how black hole mass evolves over cosmic time in a Lambda-CDM universe, accounting for both dark matter and dark energy accretion.

Contribution

It provides a closed-form model for black hole mass evolution considering cosmological fluid dynamics, improving upon previous unphysical models.

Findings

Black hole mass increases during matter-dominated era.

Mass growth halts as dark energy dominates.

Model offers a realistic transition between accretion regimes.

Abstract

The evolution of the mass of a black hole embedded in a universe filled with dark energy and cold dark matter is calculated in a closed form within a test fluid model in a Schwarzschild metric, taking into account the cosmological evolution of both fluids. The result describes exactly how accretion asymptotically switches from the matter-dominated to the Lambda-dominated regime. For early epochs, the black hole mass increases due to dark matter accretion, and on later epochs the increase in mass stops as dark energy accretion takes over. Thus, the unphysical behaviour of previous analyses is improved in this simple exact model.