Date of Award

Summer 8-15-2019

Author's School

Graduate School of Arts and Sciences

Author's Department


Degree Name

Doctor of Philosophy (PhD)

Degree Type



The growth of a black hole surrounded by dark matter can lead to a significant enhance- ment 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 a phase space analysis. 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. We also present a derivation of the two-body collision rate per four-volume in terms of the phase space distribution that can be used in any coordinate system.


English (en)

Chair and Committee

Francesc Ferrer

Committee Members

Claude W. Bernard, Renato Feres, Henric Krawczynski, Michael C. Ogilvie,


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