  We add black holes to nonrotating, spherical galaxy models, with the
assumption that the black-hole growth is slow compared with the dynamical time
but fast compared with the relaxation time. The outcome differs depending on
whether the core of the initial galaxy does or does not resemble that of an
isothermal sphere. For the isothermal case the previously-known results are
confirmed and sharpened: the black hole induces cusps in the density ($\rho\sim
r^{-3/2}$) and velocity dispersion ($v^2\sim r^{-1}$), and a tangential
anisotropy in the velocity distribution away from the center. For the
non-isothermal case the induced density cusp is steeper, and the induced
anisotropy is larger and penetrates right to the center. The cusp around the
black hole is insensitive to anisotropy in the initial velocity distribution,
and also to the origin of the black hole, unless its mass comes exclusively
from the stars of lowest angular momentum, in which case the cusp is
suppressed. We discuss the implications for the interpretation of evidence for
massive black holes in galactic nuclei.
