f-mode oscillations of anisotropic neutron stars in full general relativity

We investigate f-mode oscillations of anisotropic, nonrotating, neutron stars within the framework of full general relativity, considering linear order perturbations in both the metric and the fluid. First, we present the equations governing unperturbed stellar structures as well as oscillations under a phenomenological Ansatz to account for local anisotropy. Then, we solve those equations for two different equations of states, namely BSk21 and BSk19, the former being stiffer than the latter. For both of the cases, we consider only stable neutron stars. We see that moderately anisotropic neutron stars with the tangential pressure larger than the radial pressure can give more massive stable neutron stars than the isotropic or highly anisotropic ones. We find that the frequency of the f-mode exhibits a linear relationship with the square root of the average density of neutron stars and the slope of the linear fit depends on the anisotropic strength. We also see that, for any given value of the anisotropic strength, neutron stars of higher masses have higher values of the frequency. For lower values of the mass, the increase of the frequency with the mass is linear, but for higher values of the mass, the frequency increases rapidly with the increase in the value of the mass. However, this nonlinear rise in the frequency with the mass is not prominent when the radial pressure is larger than the tangential pressure. We also see that for a fixed value of a small mass, higher anisotropy leads to a larger value of the frequency, but when the fixed mass is above a threshold value, higher anisotropy leads to a smaller value of the frequency. Moreover, for a fixed mass of the neutron star and for the same amount of the anisotropy, the value of the frequency is higher for the softer equation of state, but the nature of the variation in the frequency with the change in the anisotropic strength is similar for the two equations of state. We also find that the damping time of the f-mode oscillation decreases as the mass of the neutron star increases for all values of the anisotropic strength. However, for mildly anisotropic neutron stars, a slight increase in the damping time occurs near the stable maximum mass. Moreover, for a fixed mass of the neutron star and for the same amount of the anisotropy, the value of the damping time is lower for the softer equation of state, but the nature of the variation in the damping time with the change in the anisotropic strength is similar for the two equations of state.