Modified gravity with logarithmic curvature corrections and the structure of relativistic stars

TL;DR

This paper investigates how a logarithmic f(R) gravity model influences the structure and observable features of relativistic stars, especially neutron stars, revealing potential deviations from General Relativity near their surfaces.

Contribution

It introduces a logarithmic f(R) gravity model motivated by quantum effects and analyzes its impact on neutron star structure, including observational signatures and the chameleon mechanism.

Findings

Chameleon effect suppresses modifications beyond a few radii from the star

Significant deviations in surface redshift near neutron star surfaces

Modified TOV equations solved for both neutron and quark stars

Abstract

We consider the effect of a logarithmic f(R) theory, motivated by the form of the one-loop effective action arising from gluons in curved spacetime, on the structure of relativistic stars. In addition to analysing the consistency constraints on the potential of the scalar degree of freedom, we discuss the possibility of observational features arising from a fifth force in the vicinity of the neutron star surface. We find that the model exhibits a chameleon effect that completely suppresses the effect of the modification on scales exceeding a few radii, but close to the surface of the neutron star, the deviation from General Relativity can significantly affect the surface redshift that determines the shift in absorption (or emission) lines. We also use the method of perturbative constraints to solve the modified Tolman-Oppenheimer-Volkov equations for normal and self-bound neutron stars (quark stars).