A non-metric scalar-core parametrization for horizonless compact objects with an operational exterior calibration

Kaykı D., YILDIZ L., GÜDEKLİ E.

European Physical Journal Plus, cilt.141, sa.8, 2026 (SCI-Expanded, Scopus)

Özet

We formulate a phenomenological scalar-core parametrization on a fixed radial configuration domain equipped with the prescribed spherical measure 4πr2dr. The core has no intrinsic Lorentzian metric, connection, causal cones, geodesics, or covariantly conserved stress–energy tensor and is not proposed as a covariant replacement for general relativity. A single spherically weighted functional generates the nonlinear static equation, while exact flux identities establish Ψ≤0, Ψ′≥0, and a centrally enhanced density response decreasing toward the interface. Static branches are calculated in flux form by adaptive shooting and independently cross-checked by collocation. For the baseline dimensionless parameters, three admissible roots are found; two are radially unstable and the shallow branch is stable, with Ψc=-0.0997737238, compactness 2M/rΣ=0.17546566, and grid-converged ω02=13.27155462. The strongest baseline residuals are ΔDE=2.220e-16, Δint=1.768e-11, and Δsolver=2.599e-11. Because the variational functional is not globally convex, stability is determined from the correctly linearized self-adjoint radial operator rather than inferred from coefficient positivity. The first ten eigenvalues are computed with finite elements and checked by an independent finite-volume discretization; the first five are refined through N=1600. Both resolved turning points are accompanied by a mesh-convergent zero-frequency mode; the lower-Φph fold lies on a branch that already contains a more negative mode. The scalar core is calibrated at r=rΣ>2M to a Schwarzschild exterior. Its weak-field correspondence is only a leading-order affine functional calibration, not a covariant general-relativistic limit. The resulting object is therefore a numerically verified horizonless compact-object parametrization with a standard exterior benchmark.