  Newly born neutron stars can present differential rotation, even if later it
should be suppressed by viscosity or a sufficiently strong magnetic field. And
in this early stage of its life, a neutron star is expected to have a strong
emission of gravitational waves, which could be influenced by the differential
rotation. We present here a new formalism for modelling differentially rotating
neutron stars: working on the slow rotation approximation and assuming a small
degree of differential rotation, we show that it is possible to separate
variables in the Einstein field equations. The dragging of inertial frames is
determined by solving three decoupled ODEs. After we establish our equilibrium
model, we explore the influence of the differential rotation on the f and
r-modes of oscillation of the neutron star in the Cowling approximation, and we
also analyze an effect of the differential rotation on the emission of
gravitational radiation from the f-modes. We see that the gravitational
radiation from the f-modes is slightly suppressed by introducing differential
rotation to the equilibrium stars.
