Fluid pulsation modes from strange stars in a higher-dimensional space-time

Abstract

In this work, we make the first step to derive non-radial pulsation equations in extra dimensions and investigate how the $f$- and $p_1$-mode frequencies of strange quark stars, within the Cowling approximation, change with the number of dimensions. In this regard, the study is performed by solving numerically the non-radial pulsation equations, adjusted for a $d$-dimensional space-time $(d\ge 4)$. We connect the interior to a Schwarzschild-Tangherlini exterior metric and analyze the $f$- and $p_1$- mode frequencies. We found that the frequencies could become higher than those found in four-dimensional space-time. The $f$-mode frequency is essentially constant and only for large gravitational radius values grows monotonically and fast with the gravitational radius. In a gravitational radius range, where $f$-mode frequencies are constant, they increase for space-time dimensions $4\le d\le 6$ and decrease for $d\ge 7$. Regarding $p_1$-mode frequencies they are always larger for higher dimensions and decay monotonically with the increase of the gravitational radius. In extra dimensions, as it happens for four-dimensional space-time, we found $p_1$-mode frequencies are always larger than the $f$-modes ones. In the Newtonian gravity, for a homogeneous star in $d$ dimensions, we observe that the $f$-mode eigenfrequencies are constant and given by the relation ${\omega }^2=lM{G}_d/R^{d-1}$; where $l$ represents the spherical harmonic index, $M{G}_d$ being the total star mass and $R$ the stellar radius.

arXiv comment12 pages, 5 figures

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Cited by in corpus (2)

• Fluid pulsation modes and tidal deformability of anisotropic strange stars in light of the GW$170817$ event
• Gravitational wave seismology of charged strange stars in the Cowling approximation: the fluid pulsation modes