A free parametrized TOV: Modified gravity from Newtonian to relativistic stars

Abstract

We test a free ad hoc parametrization of the Tolman-Oppenheimer-Volkoff (TOV) equation. We do not have in mind any specific extended theory of gravity (ETG) but each new parameter introduced has a physical interpretation. Our aim is fully pedagogical rather than a proposal for a new ETG. Given a realistic neutron star equation of state we map the contributions of each new parameter into a shift in trajectories of the mass-radius diagram. This exercise allows us to make the correspondence between each TOV sector with some possible modifications of gravity and clarifies how neutron star observations are helpful for distinguishing theories.