Information-Entropic Method: Stability of Stars and Modified Gravity Theories

Abstract

We study the stability of non-relativistic polytropic stars within two modified gravity theories i.e., Beyond Horndeski gravity and Eddington inspired Born Infeld theories using the configuration entropy method. We use spatially localized bounded function of energy density as solutions from stellar effective equations to construct the corresponding configuration entropy. We use the same argument as the one used by the authors of Refs. [1,2] that the stars are stable if there is peak in configuration entropy as a function of adiabatic index curve. Specifically, the boundary between stable and unstable regions which corresponds to Chandrasekhar stability bound is indicated from the existence of the maximum peak while the most stable polytropic stars is indicated by minimum peak in the corresponding curve. We have found that the value of critical adiabatic indexes of Chandrasekhar stability bound and the most stable polytropic stars predicted by non-relativistic limit of Beyond Horndeski Gravity and Eddington inspired Born Infeld theories are different to those predicted by general relativity where the corresponding differences depend on the free parameter of both theories.