  Annihilation radiation from neutralino dark matter at the Galactic center
(GC) would be greatly enhanced if the dark matter were strongly clustered
around the supermassive black hole (SBH). The existence of a dark-matter
"spike" is made plausible by the observed, steeply-rising stellar density near
the GC SBH. Here the time-dependent equations describing gravitational
interaction of the dark matter particles with the stars are solved. Scattering
of dark matter particles by stars would substantially lower the dark matter
density near the GC SBH over 10^10 yr, due both to kinetic heating, and to
capture of dark matter particles by the SBH. This result suggests that
enhancements in the dark matter density around a SBH would be modest whether or
not the host galaxy had experienced the scouring effects of a binary SBH.
