Extra dimensions' influence on the equilibrium and radial stability of strange quark stars

We analyze the influence of extra dimensions on the static equilibrium configurations and stability against radial perturbations. For this purpose, we solve stellar structure equations and radial perturbation equations, both modified for a $d$-dimensional spacetime ($d\geq4$) considering that spacetime outside the object is described by a Schwarzschild-Tangherlini metric. These equations are integrated considering a MIT bag model equation of state extended for $d\geq4$. We show that the spacetime dimension influences both the structure and stability of compact objects. For an interval of central energy densities $\rho_{cd}\,G_d$ and total masses $MG_d/(d-3)$, we show that the stars gain more stability when the dimension is increased. In addition, the maximum value of $M{G_d}/(d-3)$ and the zero eigenfrequency of oscillation are found with the same value of $\rho_{cd}\,G_d$; i.e., the peak value of $M{G_d}/(d-3)$ marks the onset of instability. This indicates that the necessary and sufficient conditions to recognize regions constructed by stable and unstable equilibrium configurations against radial perturbations are, respectively, $dM/d\rho_{cd}>0$ and $dM/d\rho_{cd}<0$. We obtain that some physical parameter of the compact object in a $d$-dimensional spacetime, such as the radius and the mass, depend of the normalization. Finally, within the Newtonian framework, the results show that compact objects with adiabatic index $\Gamma_1\geq2(d-2)/(d-1)$ are stable against small radial perturbations.