Realistic fluids as source for dynamically accreting black holes in a cosmological background

TL;DR

This paper demonstrates that a single imperfect fluid can generate a dynamic black hole solution in an expanding universe, with the black hole mass evolving over time due to a temperature gradient, providing insights into accreting black holes in cosmological settings.

Contribution

It introduces an exact solution to Einstein's equations where a single imperfect fluid sources a generalized McVittie metric with a time-varying mass parameter.

Findings

The solution models an accreting black hole in an expanding universe.

The mass variation is driven by a temperature gradient within the fluid.

The metric approaches Schwarzschild-de Sitter at late times.

Abstract

We show that a single imperfect fluid can be used as a source to obtain the generalized McVittie metric as an exact solution to Einstein's equations. The mass parameter in this metric varies with time thanks to a mechanism based on the presence of a temperature gradient. This fully dynamical solution is interpreted as an accreting black hole in an expanding universe if the metric asymptotes to Schwarzschild-de Sitter at temporal infinity. We present a simple but instructive example for the mass function and briefly discuss the structure of the apparent horizons and the past singularity.