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Newly born neutron stars can present differential rotation, even if later itshould be suppressed by viscosity or a sufficiently strong magnetic field. Andin this early stage of its life, a neutron star is expected to have a strongemission of gravitational waves, which could be influenced by the differentialrotation. We present here a new formalism for modelling differentially rotatingneutron stars: working on the slow rotation approximation and assuming a smalldegree of differential rotation, we show that it is possible to separatevariables in the Einstein field equations. The dragging of inertial frames isdetermined by solving three decoupled ODEs. After we establish our equilibriummodel, we explore the influence of the differential rotation on the f andr-modes of oscillation of the neutron star in the Cowling approximation, and wealso analyze an effect of the differential rotation on the emission ofgravitational radiation from the f-modes. We see that the gravitationalradiation from the f-modes is slightly suppressed by introducing differentialrotation to the equilibrium stars.

Slowly rotating neutron stars with small differential rotation: equilibrium models and oscillations in the Cowling approximation