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arXiv · 2605.13508

Quantum resolution of the Schwarzschild singularity

Vishnulal Cheriyodathillathu·Tanmay Patil·Saurya Das·Soumen Basak
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Abstract

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.

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Vishnulal Cheriyodathillathu, Tanmay Patil, Saurya Das, Soumen Basak. 2026-05-13. Quantum resolution of the Schwarzschild singularity. https://arxiv.org/abs/2605.13508

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