The number-density of stars in a spherically-symmetric system containing a massive black hole at its center

An object with a compact core is a configuration in various astrophysical problems. In this paper, considering general relativity, the number densities of stars in a spherically-symmetric system containing a massive black hole in its center has been obtained forv=4/3,5/3, and the non-relativistic case. The results obtained by Peebles (1972), Bahcall and Wolf (1976), and that obtained for an isothermal sphere case are discussed. Taking into account the stability of the system, it is found to be more rational to usen(r) r ^–7/4 to express the number density of stars when they are near the massive central black hole.