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

We give the Buchdahl's 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 $\kappa\lesssim 10^{8}\text{m}^2$ if a neutron star observed with mass around $3M_{\odot}$ can be pinned down in the future. In addition, to avoid the potential pathologies in EiBI, a \emph{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.