Impact of Anisotropy on Neutron Star Structure and Curvature

TL;DR

This study examines how pressure anisotropy influences neutron star structure and curvature, revealing that moderate anisotropy can significantly increase maximum mass and compactness while affecting curvature measures.

Contribution

It provides a detailed analysis of anisotropic effects on neutron stars using phenomenological models and compares different prescriptions, highlighting model dependence.

Findings

Moderate positive anisotropy increases maximum neutron star mass to about 2.4 solar masses.

Anisotropy can enhance stellar compactness by up to 20%.

Curvature measures sensitive to matter distribution show strong anisotropy dependence.

Abstract

We investigate the impact of pressure anisotropy on the structural and geometric properties of neutron stars within general relativity, focusing primarily on the phenomenological Bowers-Liang (BL) model, and comparing selected results with a quasi-local prescription. Using the SLy equation of state, we explore how anisotropic stresses modify global observables such as the mass-radius relation, moment of inertia, compactness, and tidal deformability over a broad range of anisotropy parameters. We find that moderate positive anisotropy can increase the maximum supported mass up to approximately $2.4\;M_\odot$ and enhance stellar compactness by up to $20\%$ relative to isotropic configurations, while remaining broadly consistent with current NICER and gravitational-wave constraints. To probe the internal gravitational field, we compute curvature invariants including the Ricci scalar, the Ricci tensor contraction, the Kretschmann scalar, and the Weyl scalar. We show that curvature measures directly tied to the matter distribution exhibit a strong sensitivity to anisotropy, whereas the Weyl curvature remains comparatively insensitive, reflecting its role as a measure of the free gravitational field. Within the phenomenological BL framework, the maximum compactness increases with anisotropy and reaches values as high as $\mathcal{C}_{\max}\approx 0.25$-$0.38$ for $\lambda_{\rm BL}\in[-4,+4]$, although the physical realizability of such highly compact configurations depends sensitively on the underlying anisotropy mechanism. A comparison with the quasi-local model highlights the strong model dependence of anisotropic effects, underscoring both the potential significance and the limitations of phenomenological anisotropy prescriptions in modeling strong-field neutron-star interiors.