Relativistic stars in f(R) and scalar-tensor theories

TL;DR

This paper investigates the structure of relativistic stars within scalar-tensor and f(R) gravity theories, demonstrating the existence of stable configurations with significant gravitational potential and constraints on the equation of state.

Contribution

It numerically constructs static relativistic star models in scalar-tensor and f(R) theories, revealing stability conditions and potential for high gravitational potential in these modified gravity models.

Findings

Maximum gravitational potential at star surface is about 0.3.

Stable configurations exist if pressure is less than one third of energy density.

Realistic neutron star equations of state satisfy the stability constraints.

Abstract

We study relativistic stars in the context of scalar tensor theories of gravity that try to account for the observed cosmic acceleration and satisfy the local gravity constraints via the chameleon mechanism. More specifically, we consider two types of models: scalar tensor theories with an inverse power law potential and f(R) theories. Using a relaxation algorithm, we construct numerically static relativistic stars, both for constant energy density configurations and for a polytropic equation of state. We can reach a gravitational potential up to $\Phi\sim 0.3$ at the surface of the star, even in f(R) theories with an "unprotected" curvature singularity. However, we find static configurations only if the pressure does not exceed one third of the energy density, except possibly in a limited region of the star (otherwise, one expects tachyonic instabilities to develop). This constraint is satisfied by realistic equations of state for neutron stars.