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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 GW170817 event and the anisotropy parameter.

We provide a summary of several parametrisations for the nuclear equation of state that have been proposed over the past decades and list viable ranges for their parameters. Based on these parametrisations, we construct a large database of rotating neutron star models using the RNS code, which are arranged in sequences of constant central energy density. After filtering these sequences with respect to generous astrophysical constraints, we discover tight universal relations for various bulk quantities of uniformly rotating neutron stars of arbitrary rotation rates. These universal relations allow bulk quantities of uniformly rotating neutron stars to be estimated at minimal computational cost, approximately three orders of magnitude faster than solving the full stellar equilibrium equations, employing only mass, radius, and moment of inertia of associated non-rotating neutron stars. Calibrated on a large, model-agnostic dataset, the relations are robust and remain accurate when tested against realistic equations of state and outperform previously published ones. For most quantities the 99th percentile of the relative residuals lies below 1.6%; the moment of inertia (2.8%) and T/W (4.6%) carry the largest uncertainties. Such relations are important for future, high-precision measurements coming from electromagnetic and gravitational wave observations and may be used in equation of state inference codes or gravitational wave modeling among others.