Effective Spacetime Geometry from Admissible Non-Injective Projection
Year: 2026
Type: preprint
Abstract: Continuing from the gauge structure established in the companion paper Q6a, we derive effective spacetime geometry from the admissibility framework of Foundation paper by importing the continuum limit and geometric-extraction theorems of the companion paper Q5b. Under the lifting hypothesis~[H-lift] of Q5b and the Mosco hypotheses of Q5a paper, the admissibility filter $\Pi_q$ converges to an effective operator $\mathcal{L}_{\mathrm{eff}}$ on $\mathbb{R}_\tau \times\mathrm{Heis}_3(\mathbb{R})$ whose principal symbol defines a four-dimensional effective metric tensor $g^{\mu\nu}(x) \propto A^{\mu\nu}(x)$ of Lorentzian signature~$(-,+,+,+)$ (Q5b Theorems~5.2 and~6.1). In the presence of a localised stationary obstruction to the admissibility flow with spherical symmetry, flux conservation within this effective geometry forces the Schwarzschild metric as the unique stationary exterior solution, with the horizon appearing as a degeneracy of the principal symbol rather than as a singularity of the underlying admissible structure. The Einstein equations emerge as consistency conditions of the emergent geometry, with the Einstein\textendash Hilbert action derived rigorously from the spectral entropy functional in the Gravity paper. The present paper closes the chain $\Pi_q \to \mathcal{L}_{\mathrm{eff}} \to g^{\mu\nu} \to G_{\mu\nu}$. No dynamical substrate is required at any step.
Author: Beau, Jérôme
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7155503073
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