  Dark matter annihilation in so-called ``spikes'' near black holes is believed
to be an important method of indirect dark matter detection. In the case of
circular particle orbits, the density profile of dark matter has a plateau at
small radii, the maximal density being limited by the annihilation
cross-section. However, in the general case of arbitrary velocity anisotropy
the situation is different. Particulary, for isotropic velocity distribution
the density profile cannot be shallower than r^{-1/2} in the very centre.
Indeed, a detailed study reveals that in many cases the term ``annihilation
plateau'' is misleading, as the density actually continues to rise towards
small radii and forms a weak cusp, rho ~ r^{-(beta+1/2)}, where beta is the
anisotropy coefficient. The annihilation flux, however, does not change much in
the latter case, if averaged over an area larger than the annihilation radius.

Astrophysics