  The Goldreich-Schubert-Fricke (GSF) instability is a rotational instability
that is thought to contribute to the transfer of angular momentum in
differentially rotating stars. It has been included in recent codes of stellar
evolution in a diffusion-like approximation, under the assumption that the
kinematic viscosity $\nu$ is unimportant for the development of the
instability. As noted previously by other authors, for most stellar
applications this may not be a valid approximation. We discuss this issue in
detail, solving the dispersion relation of the perturbed modes for realistic
values of $\nu$ in the bulk of the radiative zone of the Sun and of three red
giant stars at various evolutionary stages. We find that the GSF instability is
triggered only in layers of extremely strong shear. In a simple case study, we
also investigate the effect of a small deviation from axisymmetry or a small
background magnetic field. We find that, like the viscosity, these have a
stabilising effect. We conclude that this instability is probably far less
efficient in transporting angular momentum than is often assumed, and may not
even be present.
