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 \sim 0.8 at \sim 0.15 ~ { } \mbox { 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 .