The Buchdahl stability bound in Eddington-inspired Born-Infeld gravity

We give the Buchdahl stability bound in Eddington-inspired Born-Infeld (EiBI) gravity. We show that this bound depends on an energy condition controlled by the model parameter kappa. From this bound, we can constrain kappa less than or similar to 10(8) m(2) if a neutron star with a mass around 3M(circle dot) is observed in the future. In addition, to avoid the potential pathologies in EiBI, a Hagedorn-like equation of state associated with kappa at the center of a compact star is inevitable, which is similar to the Hagedorn temperature in string theory.