  If dark matter self-annihilates then it may produce an observable signal when
its density is high. The details depend on the intrinsic properties of dark
matter and how it clusters in space. For example, the density profile of some
dark matter candidates may rise steeply enough toward the Galactic Center that
self-annihilation produces detectable gamma-ray emission. Here, we discuss the
possibility that an annihilation signal may arise near a compact object (e.g.,
neutron star or black hole) even when the density of dark matter in the
neighborhood of the object is uniform. Gravitational focusing produces a local
enhancement of density, with a profile that falls off approximately as the
inverse square-root of distance from the compact star. While geometric dilution
may overwhelm the annihilation signal from this local enhancement, magnetic
fields tied to the compact object can increase the signal's contrast relative
to the background.
