significant enhancement of the dark matter density close to the hole. We
investigate this effect, focusing on the phenomenologically interesting case where
the black hole is supermassive and is embedded in a galactic dark matter
halo, although the formalism developed does not depend on that fact.
Due to the enhanced gravitational potential, the dark matter will tend
to cluster around the black hole. The precise details of this clustering
will, in general, depend on the formation process of the black hole.
However, if the black hole grows slowly with respect to the orbital
timescales of the local galactic potential, the density cusp only depends
on the black hole’s mass and spin, as well as on the local distribution of
orbits.
The density cusp generated by the growing black hole is called an
adiabatic spike. In the context of dark matter density cusps, these
spikes were first investigated by Gondolo and Silk (1999), using the
phase space distribution formalism. General relativistic effects
originating from the black hole’s mass were calculated by Sadeghian,
Ferrer, and Will (2013), revealing an enhancement of the density in the
spike. Our work extends this calculation to include the effects of spin.
We find a further enhancement to the spike that is strongly dependent on
the black hole’s spin parameter, meaning that it cannot be ignored for
rapidly spinning black holes. We estimate its impact in local
annihilation rates for two particular physical processes: particle dark
matter annihilation in the s-channel, and the merger rate of binaries
composed of primordial black holes in the local universe.