Moment of inertia -- compactness universal relations in scalar-tensor theories and $\mathcal{R}^2$ gravity

TL;DR

This paper explores universal relations between the moment of inertia and compactness of neutron and strange stars across various gravity theories, finding small deviations from universality and some theory independence.

Contribution

It introduces comprehensive analysis of moment of inertia-compactness relations in different gravity theories, including rapidly rotating models, highlighting their near-universality and theory independence.

Findings

Deviations from EOS universality are small across studied equations of state.

Relations are largely theory independent in some cases.

Universal relations between maximum mass and moment of inertia are also identified.

Abstract

We are investigating universal relations between different normalisations of the moment of inertia and the compactness of neutron and strange stars. Slowly rotating as well as rapidly rotating models are studied in General Relativity, $\mathcal{R}^2$ gravity and scalar--tensor theories of gravity. Moment of inertia -- compactness relations are examined for different normalisations of the moment of inertia. It is shown that for all studied cases the deviations from EOS universality are small for the examined equations of state. It turns out that in some of the cases the examined relations are also theory independent to a good extent. Universality in relations between the maximum mass and the moment of inertia for some unstable models is also investigated.