A free parametrized TOV: Modified Gravity from Newtonian to Relativistic Stars

TL;DR

This paper introduces a parametrized modification of the TOV equation to explore how different gravity theories could affect neutron star properties, providing a pedagogical tool for understanding gravity's role in stellar structure.

Contribution

It presents a free, physically interpretable parametrization of the TOV equation, linking parameters to potential gravity modifications without assuming a specific extended theory.

Findings

Parameters shift the mass-radius trajectories of neutron stars.

The approach clarifies how neutron star observations can distinguish gravity theories.

Provides a pedagogical framework for modified gravity effects in stellar models.

Abstract

We test a free {\it 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 possible modifications of gravity and clarifies how neutron star observations are helpful for distinguishing theories.