  At the cosmological stage of radiation dominance, dark matter density spikes
should form around primordial black holes. In the case when dark matter
particles are able to annihilate, the density in the central regions of the
spikes decreases due to the elimination of particles, which gives an upper
bound on the central density. In this paper, the modification of the central
density profile is investigated, taking into account the distribution of the
particle orbits. The orbits in spike around a primordial black hole are very
elongated, almost radial, and the angular momentum distribution has an
exponential form. For such an initial distribution function, it is obtained
that a cusp with the exponent $\approx-0.7$ is formed in the central region,
instead of an annihilation plateau. The presence of the cusp provides some
correction to the rate of dark matter annihilation around primordial black
holes.
