Correlation between the curvature and some properties of the neutron star

TL;DR

This study explores the relationship between surface curvature and properties of neutron stars, revealing strong correlations and establishing universal relations that help constrain neutron star characteristics using gravitational wave data.

Contribution

It introduces new correlations between surface curvature and neutron star properties, and derives universal relations linking curvature to tidal deformability, constrained by recent gravitational wave observations.

Findings

Strong cubic correlation between surface curvature and compactness for 1.4 solar mass neutron stars.

Universal relation between surface curvature and dimensionless tidal deformability.

GW190814 provides more stringent constraints on surface curvature than GW170817.

Abstract

According to the general theory of relativity, a massive body induces curvature in the surrounding spacetime. In this study, the surface curvature (SC) of neutron stars is computed using various curvature quantities derived from the relativistic mean-field, density-dependent RMF, and Skyrme-Hartree-Fock equations of states. Neutron star properties, including mass, radius, compactness, and central density, are calculated utilizing the Tolman-Oppenheimer-Volkoff equations. The analysis reveals a significant cubic correlation between the SC and compactness for the canonical 1.4 $M_{\odot}$ neutron star, with a correlation coefficient of 0.99, indicating an almost linear relationship. A similarly significant inverse cubic correlation is observed between the SC and the radius of the canonical star. However, these correlations diminish for the maximum mass NS. Furthermore, a universal relation between the SC and the dimensionless tidal deformability ($\Lambda$) for the canonical neutron star is established. Using the tidal deformability constraint of GW170817 ($\Lambda_{1.4} = 190_{-120}^{+390}$), the surface curvature is limited to SC$_{1.4} (10^{14}) = 2.87^{+0.30}_{-0.78}$ at a confidence level 90\%. Furthermore, the tidal deformability constraint of the secondary component in the GW190814 event ($\Lambda_{1.4} = 616_{-158}^{+273}$) offers a more stringent limit, with the result of SC$_{1.4} (10^{14}) = 2.03^{+0.27}_{-0.36}$. These findings indicate that the GW190814 event imposes more rigorous constraints on SC compared to GW170817.