We investigate quasi-universal relations in neutron stars linking standard observables, such as tidal deformability (Λ) and normalized moment of inertia (I), with normalized curvature scalars in general relativity. These curvature scalars include the Ricci scalar (R), the Ricci tensor contraction (J), the Weyl scalar (W), and the Kretschmann scalar (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 I and Λ; (2) especially strong correlations between surface and volume-averaged curvature scalars and both 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 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.
Danarianto et al. (Sun,) studied this question.
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