The I-Q relations for rapidly rotating neutron stars in $f(R)$ gravity

TL;DR

This paper investigates the normalized I-Q relations for neutron stars in R^2 gravity, revealing deviations from general relativity that could enable observational tests of this alternative gravity theory.

Contribution

It provides the first detailed analysis of I-Q relations in R^2 gravity for both slow and rapid rotation, highlighting significant deviations from GR.

Findings

Normalized I-Q relations are nearly EOS independent for fixed rotation

Deviations from GR can exceed 20% in R^2 gravity

Potential for observational constraints on R^2 gravity

Abstract

In the present paper we study the behavior of the normalized $I$-$Q$ relation for neutron stars in a particular class of $f(R)$ theories of gravity, namely the $R^2$ gravity that is one of the most natural and simplest extensions of general relativity in the strong field regime. We study both the slowly and rapidly rotating cases. The results show that the $I$-$Q$ relation remain nearly equation of state independent for fixed values of the normalized rotational parameter, but the deviations from universality can be a little bit larger compared to the general relativistic case. What is the most interesting in our studies, is that the differences with the pure Einstein's theory can be large reaching above 20\%. This is qualitative different from the majority of alternative theories of gravity, where the normalized $I$-$Q$ relations are almost indistinguishable from the general relativistic case, and can lead to observational constraints on the $f(R)$ theories in the future.