Stochastic Quantum Mechanics Trajectories Near Schwarzschild Horizon Black Holes

TL;DR

This paper extends stochastic quantum mechanics to curved spacetimes, specifically Schwarzschild black holes, analyzing how gravitational fluctuations influence quantum trajectories under various parameters.

Contribution

It introduces a covariant formulation of stochastic quantum equations in curved spacetime and studies scalar perturbation trajectories near black holes.

Findings

Trajectories are affected by gravitational fluctuations.

Different stochastic trajectories emerge based on parameter variations.

The approach provides insights into quantum behavior near black hole horizons.

Abstract

This work explores the possibility of applying stochastic quantum mechanics to curved spacetimes, with an emphasis on the Schwarzschild black hole. After reviewing the fundamental concepts of this approach, the quantum stochastic equations are extended to curved spacetime using a fully covariant treatment. Subsequently, the Klein-Gordon equation is solved for scalar perturbations, and the resulting stochastic trajectories are analyzed by varying parameters such as angular momentum, particle frequency, and computational integration time. In conclusion, we find that the trajectories are influenced by gravitational fluctuations in spacetime and that, depending on the variation of the fundamental parameters, different types of stochastic trajectories are obtained.