A Loop-Inspired Polymerized Chronology Equation for Axisymmetric Chronology Surfaces
Year: 2026
Type: preprint
Abstract: This corrected preprint investigates the semiclassical unfolding and dynamical evolution of a quintic inner horizon in a regular black-hole geometry supported by reconstructed magnetic nonlinear electrodynamics (NLED), coupled to an effective double-null Polyakov semiclassical model. The principal analytical result concerns the influence of asymptotic matching on the displacement of degenerate horizons. A finite-radius boundary prescription can generate a boundary-dependent leading correction. Under the specified exactly asymptotically matched characteristic conditions, this leading contribution cancels. For a degenerate horizon of order N, provided the next coefficient is nonzero and a real shifted root exists, the displacement follows the conditional scaling law: Δrₕ ∝ Lp^(4/N) For the explicit quintic geometry (N = 5), the analysis yields: Δr₋ = 0.3818443989... × Lp^(4/5) + subleading corrections. The first-order finite-boundary matching used in the numerical PDE solver instead gives a different leading coefficient, approximately 0.389528, for the specified outer boundary. This distinction is explicitly analyzed in Version 7.2. The double-null numerical calculations indicate early outward migration of the inner apparent horizon and inward migration of the outer apparent horizon. However, the grid-refinement and Richardson diagnostics do not establish a reliable continuum convergence order. Consequently, neither the late-time disappearance of apparent horizons nor a specific merger time is claimed as a demonstrated physical result. The reconstructed NLED model also exhibits a constitutive-health limitation within part of the trapped region. While this does not invalidate the algebraic derivation within the specified characteristic model, it limits the physical interpretation of the dynamical evolution. Furthermore, the Polyakov approximation retains an effective two-dimensional sector and neglects higher angular modes and other four-dimensional quantum effects. The persistence of the predicted scaling under a more complete semiclassical treatment has not been established. The main contributions of this corrected version are: A conditional scaling law for the semiclassical unfolding of degenerate inner horizons. An explicit quintic-horizon calculation with independently checked asymptotic coefficients. A clarification of the relationship between exact asymptotic matching and finite-boundary prescriptions. A numerical refinement and Richardson analysis documenting the unresolved convergence limitations. A clearer distinction between the analytical results, model-dependent assumptions, and physical interpretations. The results do not constitute a universal semiclassical stability theorem or a proof of chronology protection. This manuscript is an independent, non-peer-reviewed theoretical preprint. Version: 7.2 DOI: 10.5281/zenodo.23949538 Previous version (V7.1): https://doi.org/10.5281/zenodo.23926295
Author: Pepin, Adam
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7224488555