Stochastic Quantum Mechanics in Curved Spaces: Application to Schwarzschild Black Holes

In this work, we start from the hypothesis that the universe lives in a Gravitational Wave Background (GWB). From this hypothesis, it follows that space–time is not locally flat because we have to take into account the fluctuations of the GWB in space–time. This implies that sufficiently small particles will feel these oscillations, preventing them from following geodesic trajectories. Thus, in a previous work, it was shown that if these particles follow the geodesic trajectories plus a stochastic term due to space–time fluctuations, the field equation for these quantum particles is simply the Klein–Gordon equation in this arbitrary curved space–time. In this work, we analyze these geodesics plus the stochastic trajectories in a Schwarzschild black hole.