  The nuclear star cluster surrounding the massive black hole at the Galactic
Centre consists of young and old stars, with most of the stellar mass in an
extended, cuspy distribution of old stars. The compact cluster of young stars
was probably born in situ in a massive accretion disc around the black hole. We
investigate the effect of the growing gravity of the disc on the orbits of the
old stars, using an integrable model of the deformation of a spherical star
cluster with anisotropic velocity dispersions. A formula for the perturbed
phase space distribution function is derived using linear theory, and new
density and surface density profiles are computed. The cusp undergoes a
spheroidal deformation with the flattening increasing strongly at smaller
distances from the black hole; the intrinsic axis ratio ~ 0.8 at ~ 0.15 pc.
Stellar orbits are deformed such that they spend more time near the disc plane
and sample the dense inner parts of the disc; this could result in enhanced
stripping of the envelopes of red giant stars. Linear theory accounts only for
orbits whose apsides circulate. The non-linear theory of adiabatic capture into
resonance is needed to understand orbits whose apsides librate. The mechanism
is a generic dynamical process, and it may be common in galactic nuclei.
