Einstein Cluster as Central Spiky Distribution of Galactic Dark Matter

Abstract

Using the Einstein cluster models, we construct a fully relativistic, spherically symmetric, spiky structure of matter distribution near a supermassive black hole. We introduce and discuss three simple toy models, together with a more realistic model, which includes a Hernquist-type distribution with a typical galaxy scale. We find that the innermost stable circular orbit (ISCO) depends on the details of the environment, and lies between the photon radius (at $3M_{\mathrm{BH}}$) and the ISCO radius of an isolated black hole of mass $M_{\mathrm{BH}}$ (at $6M_{\mathrm{BH}}$).

16 pages, 13 figures