Slowly Rotating and Tidal Deformation of Nonlocal Modified Tolman VII Star

TL;DR

This paper studies the effects of nonlocal gravity on rotating and tidally deformed neutron stars, deriving key properties and comparing them with observational data, revealing the influence of nonlocal parameters on star characteristics.

Contribution

It introduces a nonlocal gravity framework to analyze neutron star properties, deriving new relations and examining observational constraints, which is a novel approach in this context.

Findings

Results are consistent with tidal constraints for certain nonlocal parameters.

Nonlocal parameter significantly influences star radius.

Universal I-Love-Q relations hold for fixed nonlocal parameters, but not when varying them.

Abstract

We investigate the moment of inertia, quadrupole deformation, and tidal deformation within the framework of nonlocal gravity, utilizing the exact modified Tolman-VII (NEMTVII) density model with an isotropic perfect fluid. The Love number~$(k_{2})$ is derived using standard even-parity perturbation theory. Additionally, we explore the observational implications by analyzing the tidal deformability parameter~$( \lambda_{\textrm{tid}} )$ in comparison with the constraints from GW170817, GW190425, PSR J0348+0432, and PSR J0740+6620. We found that the results are consistent with the tidal constraint when $\alpha \gtrsim 1.6$ with the small $\beta$. For slowly rotating object, the dimensionless moment of inertia~$( \bar{I} )$, rotational Love parameter~$( \bar{\lambda}_{\textrm{rot}} )$, and quadrupole moment~$( \bar{Q} )$ are fully determined by the perturbed metric. Our findings reveal that the nonlocal parameter~$( \beta )$ significantly affects the star radius. For a fixed $\beta$ and varying $\alpha$, the $I$-Love-$Q$ relations are found to be universal. For varying $\beta$, the $I$-Love-$Q$ relations become non-universal.