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

Abstract

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 ($d\ge 4$) 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 $d\ge 4$. 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 $M{G}_d/(d-3)$, 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 ${\Gamma }_1\ge 2(d-2)/(d-1)$ are stable against small radial perturbations.

10 Pages, 8 figures

References in corpus (6)

• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• White dwarf stars in D dimensions
• Bonnor stars in d spacetime dimensions
• Electrically charged fluids with pressure in Newtonian gravitation and general relativity in d spacetime dimensions: theorems and results for Weyl type systems
• Stability of thin-shell interfaces inside compact stars
• Radial stability in stratified stars

Cited by in corpus (4)

• Five-dimensional compact stars in Einstein-Gauss-Bonnet gravity
• Fluid pulsation modes from strange stars in a higher-dimensional space-time
• Oscillatory properties of strange quark stars described by the vector MIT bag model
• On the Dynamical Instability of Monatomic Fluid Spheres in (N+1)-Dimensional Spacetime