Abstract
Young neutron stars formed in core collapse or originating in the merger of a binary neutron star system may possess significant differential rotation. We consider the stability properties of such hot (non-superfluid) differentially rotating neutron stars. Compared to ordinary stars, the criteria of hydrodynamic instability of neutron stars can be different because generally the thermal diffusivity and viscosity are of the same order of magnitude and are relatively large. For example, the well-known Goldreich-Schubert instability can manifest itself only in rapidly rotating stars and is strongly suppressed if rotation is slow. The rotational instabilities in neutron stars can grow on the thermal or dynamical timescale.
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