Examining the influence of anisotropy on the fundamental mode of nonradial oscillation in neutron stars on a complete general relativistic scheme

The anisotropic influence on the $f$-mode frequency of oscillations and dimensionless tidal deformability of neutron stars is analyzed by employing the nonradial oscillation equations for the complete general relativity frame and tidal deformability equations, which are derived and modified from their standard form to introduce the anisotropic factor. The fluid inside the compact star obeys an equation of state constructed by matching microscopic nuclear and perturbative QCD calculations through a piecewise polytropic interpolating scheme. For the anisotropic profile, we use a local anisotropy which is regular along the whole star and vanishes both at the center and on the star's surface. We show that the \(f\)-mode oscillation frequency and dimensionless tidal deformability are noticeably affected by anisotropy. Finally, we investigate the correlation between the dimensionless tidal deformability inferred from the GW$170817$ event and the anisotropy parameter.