Quasi-normal f-modes of anisotropic quark stars in full general relativity

We investigate f-mode oscillations of anisotropic quark stars within the framework of full general relativity. We consider two different equations of state (EOSs), one is the MIT bag model EOS and the other is EOS-A. Our study examines the impact of the pressure anisotropy on the equilibrium structure, as well as on the frequencies and damping times of f-mode oscillations. Our results confirm that the f-mode frequency scales linearly with the square root of the average density, with anisotropy influencing both the slope and intercept of this relation. The dependence of the f-mode frequency on total mass reveals distinct trends based on the relative dominance of tangential and radial pressure. When the tangential pressure exceeds the radial pressure, the frequency increases with mass, exhibiting rapid growth for massive quark stars. When the radial pressure dominates, the frequency increases with mass; however, in cases where the radial pressure is significantly greater than the tangential pressure, the frequency decreases as mass increases. For low-mass quark stars, stronger tangential pressure leads to an increase in frequency, while beyond a threshold mass, a further increase in tangential pressure results in a decrease in frequency. For the chosen range of anisotropic strengths, the frequency varies between 1.3 kHz and 2.3 kHz for the MIT bag EOS and between 1.8 kHz and 3.4 kHz for EOS-A. We find that the normalized damping time follows a linear trend with compactness. For a fixed stellar mass, an increase in tangential pressure relative to radial pressure reduces the damping time, whereas a decrease in tangential pressure significantly increases it. The damping time ranges from 83 ms to 900 ms for the MIT bag EOS and from 60 ms to 761 ms for EOS-A. We present semi-empirical expressions for both the frequency and damping time as functions of mass, radius, and anisotropic strength.