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Theory of Curvature-Driven Wavefunction Collapse and Primordial Black Hole Survival

mirwais khan

Published Aug 7, 2025• 0 citations
OpenAlex

Abstract

This paper proposes a quantum mechanical collapse model driven by spacetime curvature, formulated through a modified Schrödinger equation in Schwarzschild spacetime. The collapse criterion is based on a curvature amplification factor derived from the Klein–Gordon equation. We demonstrate how this theory suppresses Hawking radiation in low-mass black holes and explains the 2–5 solar mass gap seen in LIGO/Virgo gravitational wave detections. The proposed framework offers a speculative but testable path toward unifying aspects of quantum collapse and black hole thermodynamics.

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We revisit the Schwarzschild singularity in a semiclassical setting where the background geometry is classical and quantum effects enter through Bohmian (quantal) trajectories associated with a Klein Gordon wave packet. Using the Madelung-Bohm decomposition of the Klein Gordon wavefunction, we show that the quantum-modified motion is equivalent to geodesic motion in an effective metric conformally related to Schwarzschild, with a conformal factor fixed by the wavefunction amplitude. Solving the wavefunction equation near $r\to 0$ determines this factor and yields finite curvature invariants, in suitable coordinates the interior extends smoothly and the effective spacetime is geodesically complete. This suggests that quantum dynamics on a fixed classical background can regularize the Schwarzschild singularity without a full theory of quantum gravity.

gr-qcCross-listedarXiv:2605.13508•May 14, 2026
This paper proposes a quantum mechanical collapse model driven by spacetime curvature, formulated through a modified Schrödinger equation in Schwarzschild spacetime. The collapse criterion is based on a curvature amplification factor derived from the Klein–Gordon equation. We demonstrate how this theory suppresses Hawking radiation in low-mass black holes and explains the 2–5 solar mass gap seen in LIGO/Virgo gravitational wave detections. The proposed framework offers a speculative but testable path toward unifying aspects of quantum collapse and black hole thermodynamics.
In this paper, the authors propose a phenomenological framework for addressing the black hole information loss paradox using the Gravity Branch Model (GBM) of quantum measurements. In this approach, quantum measurement branching is dynamically constrained by local spacetime curvature, producing effective selection of semiclassically consistent trajectories. We develop Schrödinger-like and master equation formulations for the GBM, apply it to a detector of Hawking radiation, and examine how gravitationally suppressed branch proliferation modifies the apparent information content. Our analysis suggests that information loss in black holes can be reinterpreted as curvature-induced pruning of quantum measurement branches, rather than fundamental nonunitarity, with experimentally constrained coupling strengths ensuring consistency with laboratory observations.
This work proposes the Collapse Clock Hypothesis, a framework in which physical time is defined by the rate of irreversible wavefunction collapse, interpreted as a process of information pruning constrained by finite informational capacity. Within this framework, spatial variations in collapse rate give rise to differential progression of proper time, providing a potential mechanism for gravitational time dilation and related phenomena. The approach integrates concepts from quantum information theory, thermodynamics, and emergent spacetime, drawing connections to prior work on entanglement entropy, holographic bounds, and thermodynamic derivations of gravitational dynamics. A computational implementation using a Score-Driven Kinetic Ising Model (SDKIM) is presented to explore whether the proposed causal chain—mass → interactions → entanglement → collapse suppression → slower time—can arise dynamically in a simplified lattice system. The simulations demonstrate robust qualitative behavior consistent with collapse-rate suppression in highly entangled regions, while also highlighting important limitations, including the use of mean-field approximations and the absence of a direct quantitative mapping to known gravitational field equations. This work is intended as a speculative but testable framework rather than a complete theory. Several falsifiable predictions are outlined, including potential signatures in precision timekeeping, quantum-coherent systems, gravitational wave phase evolution, and cosmological observables. These predictions are presented at an order-of-magnitude level and require further development for direct comparison with experimental data. The goal of this work is to explore whether irreversible information dynamics may provide a unifying underlying mechanism for time, gravity, and cosmological evolution, and to motivate further investigation into collapse-based approaches to fundamental physics.
We consider the black hole information problem within the context of collapse theories in a scheme that allows the incorporation of the backreaction to the Hawking radiation. We explore the issue in a setting of the two dimensional version of black hole evaporation known as the Russo-Susskind-Thorlacius model. We summarize the general ideas based on the semiclassical version of Einstein’s equations and then discuss specific modifications that are required in the context of collapse theories when applied to this model.
Primordial black holes (PBHs) form when large primordial curvature perturbations re-enter the Hubble radius and exceed the classical collapse threshold. These perturbations originate as quantum fluctuations of the inflationary vacuum, motivating a quantum-information description of the PBH-producing scalar sector. We develop a conservative extension of the standard PBH and scalar-induced gravitational-wave (SIGW) framework in which Gaussian quantum discord is used as a diagnostic of residual quantum correlations, not as a new PBH-formation criterion. We describe each (k,−k)(\bm k,-\bm k)(k,−k) pair as a two-mode Gaussian state and show that, in the pure squeezed limit, discord grows rapidly with the squeezing parameter, so low discord thresholds are automatically satisfied for strongly squeezed modes. The nontrivial regime is the mixed state produced by decoherence. Using a Lindblad open-system description, we motivate a Gaussian loss channel for the scalar covariance matrix and distinguish the discord from a covariance-survival factor Qdec(k)Q_{\rm dec}(k)Qdec​(k). If the decoherence channel suppresses the scalar two-point covariance, PBH abundance can be affected through the classical collapse variance, while the SIGW spectrum is modified more directly by the factors Qdec(ku)Qdec(kv)Q_{\rm dec}(ku)Q_{\rm dec}(kv)Qdec​(ku)Qdec​(kv) inside the radiation-era convolution. For a narrow scalar peak and slowly varying QdecQ_{\rm dec}Qdec​, this gives the benchmark scaling ΩGWeff≃Qdec2ΩGWclassΩ_{\rm GW}^{\rm eff}\simeq Q_{\rm dec}^2Ω_{\rm GW}^{\rm class}ΩGWeff​≃Qdec2​ΩGWclass​. Thus quantum discord and decoherence provide a controlled way to characterize the quantum-to-classical transition of PBH-producing perturbations, with the clearest imprint appearing in scalar-induced gravitational waves.
Inspired by an ontic view of the wavefunction in quantum mechanics and motivated by the universal interaction of gravity, we discuss a possible gravity implication in the state collapse mechanism. Concretely, we investigate the stability of the spatial superposition of a massive quantum state under the gravity effect. In this context, we argue that the stability of the spatially superposed state depends on its gravitational self-energy originating from the effective mass density distribution through the spatially localized eigenstates. We reveal that the gravitational self-interaction between the different spacetime curvatures created by the eigenstate effective masses leads to the reduction of the superposed state to one of the possible localized states. Among others, we discuss such a gravity-driven state reduction. Then, we approach the corresponding collapse time and the induced effective electric current in the case of a charged state, as well as the possible detection aspects.
We revisit the Schwarzschild singularity in a semiclassical setting where the background geometry is classical and quantum effects enter through Bohmian (quantal) trajectories associated with a Klein Gordon wave packet. Using the Madelung-Bohm decomposition of the Klein Gordon wavefunction, we show that the quantum-modified motion is equivalent to geodesic motion in an effective metric conformally related to Schwarzschild, with a conformal factor fixed by the wavefunction amplitude. Solving the wavefunction equation near r→0r\to 0r→0 determines this factor and yields finite curvature invariants, in suitable coordinates the interior extends smoothly and the effective spacetime is geodesically complete. This suggests that quantum dynamics on a fixed classical background can regularize the Schwarzschild singularity without a full theory of quantum gravity.