Abstract
We study the hydrostatic equilibrium structure of compact stars in the Eddington-inspired Born-Infeld gravity recently proposed by Ba\~nados and Ferreira [Phys. Rev. Lett. 105, 011101 (2010)]. We also develop a framework to study the radial perturbations and stability of compact stars in this theory. We find that the standard results of stellar stability still hold in this theory. The frequency square of the fundamental oscillation mode vanishes for the maximum-mass stellar configuration. The dependence of the oscillation mode frequencies on the coupling parameter $\ensuremath{\kappa}$ of the theory is also investigated. We find that the fundamental mode is insensitive to the value of $\ensuremath{\kappa}$, while higher-order modes depend more strongly on $\ensuremath{\kappa}$.
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