The Buchdahl Stability Bound in Eddington-inspired Born-Infeld Gravity

TL;DR

This paper derives the Buchdahl stability bound within EiBI gravity, showing its dependence on a model parameter and proposing constraints on this parameter based on neutron star observations, while also discussing potential pathologies.

Contribution

It presents the first derivation of the Buchdahl bound in EiBI gravity and links it to observational constraints and theoretical pathologies.

Findings

Bound depends on energy condition controlled by $1$

Constraints on $1$ from neutron star mass observations

Necessity of Hagedorn-like equation of state to avoid pathologies

Abstract

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 $\kappa\lesssim 10^{8}\text{m}^2$ if a neutron star with a mass around $3M_{\odot}$ is observed 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.