A Decoherence-Based Effective Framework for Singularity Reinterpretation in Black-Hole Interiors
Abstract
Abstract Classical general relativity predicts that gravitational collapse may terminate in geodesicincompleteness and divergent curvature. In this work we develop a conservative effectiveframework in which this classical singular behavior is not merely removed, butreinterpreted as the failure of a smooth coherent spacetime phase---what we might thinkof, in some sense, as the ``boiling'' of the spacetime fabric itself at Planck-scaledensities, where the connections between its fundamental grains are severed. Weintroduce a complex spacetime coherence order parameter \((\Psi = |\Psi|e^{i\theta})\),define a bounded decoherence variable \((D = 1 - |\Psi|^2/|\Psi_0|^2)\), and formulate acurvature-sensitive effective action. A central correction in the present formulation isthat the fundamental regular amplitude variable is \((\varphi = |\Psi|/|\Psi_0|)\), while\((D = 1 - \varphi^2)\) is a useful but singular coordinate on field space near maximaldecoherence; the apparent factor \(((1-D)^{-1})\) in the \((D)\)-gradient stress is thereforenot a physical divergence but a field-coordinate artifact, handled either in terms of\((\varphi)\) or by a regulated interface profile. Curvature suppresses the coherenceamplitude through an invariant diagnostic \((\mathcal{I}[g])\), allowing the use of theKretschmann invariant in black-hole collapse rather than restricting the model to theRicci scalar, which vanishes in vacuum Schwarzschild spacetime and therefore fails tocapture tidal curvature.…
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