Solutions of the Einstein Equations for a Black Hole Surrounded by a Galactic Halo

Abstract

Various profiles of matter distribution in galactic halos (such as the Navarro–Frenk–White, Burkert, Hernquist, Moore, Taylor–Silk models, and others) are considered here as the source term for the Einstein equations. We solve these equations and find exact solutions that 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 metrics, which include 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.