Speaker
Description
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 $(d\geq4)$. 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 $4\leq d\leq6$ and decrease for $d\geq7$. 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 $\omega^2=l\, M\, G_d/R^{d-1}$; where $l$ represents the spherical harmonic index, $M\,G_d$ being the total star mass and $R$ the stellar radius. For some gravitational radius interval, we show that a homogeneous star in Newtonian gravity is a good approximation to investigate the $f$-mode frequency of strange stars in the relativistic frame. In each dimension considered, we find that the $f$-mode frequencies are essentially constant since they depend on the average star density that is almost constant for strange quark stars. Moreover, for a fixed energy density, we also find that the $f$-mode frequency changes with the volume of the unitary sphere in $d-1$ dimension, which attains its maximum value at $d=6$. In neutron stars in four-dimensions, where the average energy density of the star increase with the central energy density, the $f$-mode frequencies will increase with the star mass. Thus, the possibility of measure in gravitational wave detectors the $f$-mode oscillation frequency coming from compact stars with different pulsar masses and observe almost constant frequency values, for $d=4$, in the range $f\sim2-3\,[\rm kHz]$ with $ M\leq1.8M_\odot$, it would be a good signature of the existence of strange quark stars that still lack an astronomical confirmation. Finally, if the $f$-mode frequencies are still constant and greater than $d=4$ range for larger total masses, it would be an evidence that quarks can propagate in extra space-time dimensions and strange quarks stars in $d$ dimension could exist.
