Stellar oscillations in Eddington-inspired Born-Infeld gravity

Abstract

We consider the stellar oscillations of relativistic stars in the Eddington-inspired Born-Infeld gravity (EiBI). In order to examine the specific frequencies, we derive the perturbation equations governing the stellar oscillations in EiBI by linearizing the field equations and numerically determine the oscillation frequencies by changing the coupling parameter in EiBI, $\ensuremath{\kappa}$, and stellar models. As a result, we find that the frequencies depend strongly on the value of $\ensuremath{\kappa}$, where the frequencies in EiBI with negative $\ensuremath{\kappa}$ become higher and those with positive $\ensuremath{\kappa}$ become lower than the expectations in general relativity. We also find that, via the observation of the fundamental frequency, one could distinguish EiBI with $8\ensuremath{\pi}{\ensuremath{\epsilon}}_{0}|\ensuremath{\kappa}|\ensuremath{\gtrsim}0.03$ from general relativity, independently of the equation of state for neutron star matter, where ${\ensuremath{\epsilon}}_{0}$ denotes the nuclear saturation density and ${\ensuremath{\epsilon}}_{0}\ensuremath{\kappa}$ becomes a dimensionless parameter. With the further constraints on equation of state, one might distinguish EiBI even with $8\ensuremath{\pi}{\ensuremath{\epsilon}}_{0}|\ensuremath{\kappa}|\ensuremath{\lesssim}0.03$ from general relativity.