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≥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≥4. We show that the spacetime dimension influences both the structure and the stability of compact objects. For an interval of central energy densities ρcdGd and total masses MGd/(d-3), we show that the stars gain more stability when the dimension is increased. In addition, the maximum value of MGd/(d-3) and the zero eigenfrequency of oscillation are found with the same value of ρcdGd; i.e., the peak value of MGd/(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/dρcd>0 and dM/dρcd<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 Γ1≥2(d-2)/(d-1) are stable against small radial perturbations.
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We would like to thank Fundação de Amparo à Pesquisa do São Paulo-FAPESP for Grant No. 2013/26258-4. J. D. V. A. thanks Vilson T. Zanchin for the enriching discussions about the influence of higher dimensions in the configuration of some compact objects. G. A. C. and R. V. L. thank Coordenação de Aperfeiçoamento de Pessoal de Nível Superior-CAPES for Grants No. CAPES/PDSE/88881.188302/2018-01 and No. CAPES/PDSE/88881.134089/2016-01, respectively. R. V. L. also thanks Conselho Nacional de Desenvolvimeno Científico e Tecnológico-CNPq for Grant No. 141157/2015-1.
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