$I-$Love$-$Curvature: Exploring compact stars' quasi-universal relation with curvature scalars
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| Format: | Preprint |
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2025
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| author | Danarianto, M. D. Sulaksono, A. |
| author_facet | Danarianto, M. D. Sulaksono, A. |
| contents | We investigate quasi-universal relations in neutron stars linking standard observables, such as tidal deformability ($Λ$) and normalized moment of inertia ($\bar{I}$), with normalized curvature scalars in general relativity. These curvature scalars include the Ricci scalar ($\mathcal{R}$), the Ricci tensor contraction ($\mathcal{J}$), the Weyl scalar ($\mathcal{W}$), and the Kretschmann scalar ($\mathcal{K}$). We systematically examine both piecewise polytropic and color-flavor-locked equations of state, finding: (1) significant correlations between both local (central and surface) and global (volume-averaged) curvature scalars with $\bar{I}$ and $Λ$; (2) especially strong correlations between surface and volume-averaged curvature scalars and both $\bar{I}$ and $Λ$; (3) a near equation-of-state-independent maximum for the normalized Ricci scalar, suggesting a link to the trace anomaly; and (4) new universal relations involving normalized central and volume-averaged pressure and energy density, which also correlate strongly with $\bar{I}$ and $Λ$. Using constraints from GW170817 and low-mass X-ray binaries, we demonstrate that $Λ$ measurements directly constrain both scalar curvature quantities and the interior properties of canonical-mass neutron stars. These findings agree with the literature on equation-of-state-dependent Bayesian inference estimates. Our identified relations thus provide an equation-of-state-insensitive connection between stellar observables, spacetime geometry, and the microphysics of compact stars. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_04260 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $I-$Love$-$Curvature: Exploring compact stars' quasi-universal relation with curvature scalars Danarianto, M. D. Sulaksono, A. General Relativity and Quantum Cosmology We investigate quasi-universal relations in neutron stars linking standard observables, such as tidal deformability ($Λ$) and normalized moment of inertia ($\bar{I}$), with normalized curvature scalars in general relativity. These curvature scalars include the Ricci scalar ($\mathcal{R}$), the Ricci tensor contraction ($\mathcal{J}$), the Weyl scalar ($\mathcal{W}$), and the Kretschmann scalar ($\mathcal{K}$). We systematically examine both piecewise polytropic and color-flavor-locked equations of state, finding: (1) significant correlations between both local (central and surface) and global (volume-averaged) curvature scalars with $\bar{I}$ and $Λ$; (2) especially strong correlations between surface and volume-averaged curvature scalars and both $\bar{I}$ and $Λ$; (3) a near equation-of-state-independent maximum for the normalized Ricci scalar, suggesting a link to the trace anomaly; and (4) new universal relations involving normalized central and volume-averaged pressure and energy density, which also correlate strongly with $\bar{I}$ and $Λ$. Using constraints from GW170817 and low-mass X-ray binaries, we demonstrate that $Λ$ measurements directly constrain both scalar curvature quantities and the interior properties of canonical-mass neutron stars. These findings agree with the literature on equation-of-state-dependent Bayesian inference estimates. Our identified relations thus provide an equation-of-state-insensitive connection between stellar observables, spacetime geometry, and the microphysics of compact stars. |
| title | $I-$Love$-$Curvature: Exploring compact stars' quasi-universal relation with curvature scalars |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2510.04260 |