Solutions of the Einstein equations for a black hole surrounded by a galactic halo

TL;DR

This paper derives exact and analytical solutions to Einstein's equations for black holes embedded in galactic halos with various matter distribution profiles, enhancing understanding of such astrophysical systems.

Contribution

It provides the first comprehensive set of analytical metrics for black holes in galactic halos considering multiple matter profiles, bridging numerical and analytical approaches.

Findings

Exact solutions for black holes in galactic halos are obtained.

Analytical metrics are derived for astrophysically relevant regimes.

The solutions encompass various matter distribution models.

Abstract

Various profiles of matter distribution in galactic halos (such as Navarro-Frenk-White, Burkert, Hernquist, Moore, Taylor-Silk and others) are considered here as the source term for the Einstein equations. We solve these equations and find exact solutions which represent the metric of a central black hole immersed in a galactic halo. Even though in the general case the solution is numerical, very accurate general analytical metric, which includes all the particular models, are found in the astrophysically relevant regime, when the mass of the galaxy is much smaller than the characteristic scale in the halo.