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We analyze the influence of extra dimensions on the static equilibriumconfigurations and stability against radial perturbations. For this purpose, wesolve stellar structure equations and radial perturbation equations, bothmodified for a $d$-dimensional spacetime ($d\geq4$) considering that spacetimeoutside the object is described by a Schwarzschild-Tangherlini metric. Theseequations are integrated considering a MIT bag model equation of state extendedfor $d\geq4$. We show that the spacetime dimension influences both thestructure and stability of compact objects. For an interval of central energydensities $\rho_{cd}\,G_d$ and total masses $MG_d/(d-3)$, we show that thestars gain more stability when the dimension is increased. In addition, themaximum value of $M{G_d}/(d-3)$ and the zero eigenfrequency of oscillation arefound 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 thenecessary and sufficient conditions to recognize regions constructed by stableand unstable equilibrium configurations against radial perturbations are,respectively, $dM/d\rho_{cd}>0$ and $dM/d\rho_{cd}<0$. We obtain that somephysical parameter of the compact object in a $d$-dimensional spacetime, suchas the radius and the mass, depend of the normalization. Finally, within theNewtonian framework, the results show that compact objects with adiabatic index$\Gamma_1\geq2(d-2)/(d-1)$ are stable against small radial perturbations.

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