Bound orbits around a black hole surrounded by a galaxy
Motivated by recent work investigating the properties of black holes in galaxies, we investigate a galactic configuration comprising a central black hole with a Hernquist-like mass distribution. Unlike previous work, we incorporate the galactic potential into the black hole metric in isotropic coordinates, which is more appropriate when taking the Newtonian limit. We calculate corrections to Schwarzschild quantities as functions of the compactness of the galaxy. As the compactness increases, our analysis reveals a decrease in the radius of the innermost stable circular orbit, along with an increase in the number of potential stable orbital configurations around a central black hole inside a galaxy.