Quantum resolution of the Schwarzschild singularity

TL;DR

This paper demonstrates that quantum effects modeled via Bohmian trajectories can smooth out the Schwarzschild singularity, resulting in a regular, geodesically complete spacetime without requiring a full quantum gravity theory.

Contribution

It introduces a semiclassical approach using Bohmian trajectories to resolve the Schwarzschild singularity by deriving an effective metric that remains finite at the core.

Findings

Quantum-modified trajectories lead to finite curvature invariants.

The effective metric extends smoothly through the classical singularity.

The interior spacetime becomes geodesically complete.

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.