Abstract:
Compact stars, such as neutron stars and quark stars, provide a unique environment for studying matter at extreme densities, though the underlying physics remains uncertain due to limitations in the equations of state (EoS). Gravitational waves (GWs), particularly those arising from quasi-normal modes (QNMs), offer a powerful probe of their internal structure. Among these, the fundamental (f-mode) oscillations are especially significant due to their strong coupling with gravitational radiation and sensitivity to stellar properties.This study presents a fully relativistic analysis of f-mode oscillations in anisotropic compact stars using general relativistic perturbation theory. Unlike earlier approaches based on isotropy or simplifying assumptions such as the Cowling approximation, both fluid and spacetime perturbations are included. Pressure anisotropy, motivated by physical effects such as superfluidity, magnetic fields, and pion condensation, is examined for neutron and quark stars with realistic EoS.Equilibrium configurations are constructed by extending the Tolman–Oppenheimer–Volkoff equations to incorporate anisotropy. The perturbation equations for non-radial oscillations are derived by linearizing Einstein’s field equations and solved numerically with appropriate boundary conditions.The results show that the f-mode frequency retains an approximately linear dependence on the square root of the average density, with anisotropy modifying the relation. Frequency increases with anisotropy at lower masses but decreases at higher masses, while the damping time decreases monotonically. Variations of up to ~20% in frequency and ~300% in damping time are observed compared to isotropic cases. The inverse normalized damping time also shows a linear dependence on compactness.Semi-empirical relations are developed linking frequency and damping time to mass, radius, and anisotropy. The frequency exhibits cubic dependence on anisotropy, while the damping time shows sextic dependence for neutron stars and quartic for quark stars.Overall, this work demonstrates that pressure anisotropy significantly affects the quasi-normal mode spectrum of compact stars and highlights its importance in gravitational wave astronomy and future astrophysical modeling.
