Non-radial oscillations of anisotropic neutron stars in the Cowling approximation

One of the most common assumptions in the study of neutron star models and their oscillations is that the pressure is isotopic, however there are arguments that this may not be correct. Thus in the present paper we make a first step towards studying the nonradial oscillations of neutron stars with an anisotropic pressure. We adopt the so-called Cowling approximation where the spacetime metric is kept fixed and the oscillation spectrum for the first few fluid modes is obtained. The effect of the anisotropy on the frequencies is apparent, although with the present results it might be hard to distinguish it from the changes in the frequencies caused by different equations of state.