  Differential rotation plays a key role in stellar evolution by triggering
hydrodynamical instabilities and large-scale motions that induce transport of
chemicals and angular momentum and by modifying the propagation and the
frequency spectrum of gravito-inertial waves. It is thus crucial to investigate
its effect on the propagation of gravity waves to build reliable seismic
diagnostic tools, especially for fast rotating stars, where perturbative
treatments of rotation fail. Generalising a previous work done in the case of
uniform rotation, we derived a local dispersion relation for gravity waves in a
differentially rotating star, taking the full effect of rotation (both Coriolis
and centrifugal accelerations) into account. Then we modelled the propagation
of axisymmetric waves as the propagation of rays. This allowed us to
efficiently probe the properties of the waves in various regimes of
differential rotation.
