Impact of Anisotropy on Neutron Star Structure and Curvature

TL;DR

This work investigates how pressure anisotropy influences neutron star structure and curvature within general relativity, using the phenomenological Bowers–Liang model with the SLy equation of state. By computing mass–radius relations, moment of inertia, tidal deformability, and a set of curvature invariants, the authors show that moderate positive anisotropy can raise the maximum mass to about $2.4\,M_\odot$ and increase compactness to roughly $C_{\max} \sim 0.25$–$0.38$, while the Weyl curvature remains less sensitive to anisotropy. Curvature measures tied to matter distribution (Ricci scalar, contraction, Kretschmann) exhibit strong anisotropy sensitivity, highlighting the role of interior matter in strong-field gravity; in contrast, Weyl curvature reflects the free gravitational field with weaker anisotropy response. A comparison with a quasi-local anisotropy model reveals substantial model dependence of anisotropic effects, underscoring both the potential significance and the limitations of phenomenological anisotropy prescriptions when interpreting NICER and gravitational-wave observations.

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 $λ_{\rm BL}\in[-4,+4]$, 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.

Figures (9)

• Figure 1: Panel (a): Tangential pressure as a function of the radial coordinate for a star with different values of $\lambda_{\text{BL}}$. The black dashed line corresponds to the isotropic case. Panel (b): Anisotropy factor, $\sigma$, as a function of the radial coordinate for the SLy EoS.
• Figure 2: The radial profile of the tangential sound speed ($c_{s\perp}$) with the SLy EoS for various $\lambda_{\rm BL}$ values at fixed central density. The conformal limit is shown by the dashed green line.
• Figure 3: Panel (a): Impact of anisotropy on the mass–radius relation of NSs, illustrated for the BL model. The plot includes constraints from recent observations, namely the NICER measurements of PSR J0030+0451 riley_2019nicermiller_2019psr and PSR J0740+6620 miller_2021, the gravitational-wave events GW170817 abbott_2017abbott_2019, GW190814 abbott_2020, GW200105, and GW200115 abbott_2021, as well as precise radio pulsar mass determinations such as PSR J0348+0432 antoniadis_2013. Panel (b): Mass as a function of central density for different values of $\lambda_{\text{BL}}$. Filled circles show maximum on $M-\mathcal{E}_c$ curves. Configuration to the right of the maxima (dotted segments) are unstable ($\mathrm{d} M/\mathrm{d}\mathcal{E}_c < 0$) with respect to small radial perturbation.
• Figure 4: Panel (a): Moment of inertia of NSs as a function of mass for different values of $\lambda_{\text{BL}}$. The error bars correspond to observational constraints from pulsar analyses of double NSr systems (DNS), low-mass X-ray binaries (LMXB), and millisecond pulsars (MSP), as reported in Ref. kumar_2019. Panel (b): Moment of inertia of NSs as a function of central density for different values of $\lambda_{\text{BL}}$.
• Figure 5: Tidal properties of NSs calculated for anisotropy parameters $\lambda_{\rm BL} \in[-2.0 ,+2.0]$ using the SLy EoS. Upper panels: (a) dimensionless tidal deformability $\Lambda$ versus mass, error bars obtained from the tidal deformability of LMXB, MSP, and DNS based on GW170817 data with universal relations are shown with observational constraints kumar_2019. The mass range from GW190425 is shown by the gray vertical band, and for GW170817, various posteriors correlate to different methodologies and confidence levels abbott_2017abbott_2018abbott_2019abbott_2020gw190425. (b) tidal deformability $\bm{\lambda}$ versus mass. The gray region depicts the 90% confidence upper limit on $\Lambda$ from X-ray and LIGO data for a binary of two nonrotating $1.4\,M_\odot$ NSs at 50 Mpc, with no tidal phase shift.The olive horizontal band represents the observational constraint from GW170817 for a $1.4\,M_\odot$ NS flanagan_2008hinderer_2008. Lower panels: (c) dimensionless tidal Love number $k_2$ versus mass, (d) $k_2$ versus compactness $C$.