Quantum Back Flow Across a Black Hole Horizon in a Toy Model Approach

TL;DR

This paper investigates quantum back flow across a black hole horizon using a toy model, revealing non-classical probability flow phenomena that challenge classical notions of information loss.

Contribution

It introduces a simplified model to demonstrate quantum back flow near black hole horizons, highlighting quantum effects in black hole physics.

Findings

Quantum back flow occurs near the black hole horizon.

Classical loss of information is challenged by quantum effects.

Back flow observed in Rindler spacetime as well.

Abstract

Quantum Back Flow (QBF), discovered quite a few years back, is a generic purely quantum phenomenon, in which the probability of finding a particle in a direction is non-zero (and increasing for a certain period of time) even when the particle has with certainty a velocity in the opposite direction. In this paper, we study QBF of a quantum particle across the event horizon of a Schwarzschild Black Hole. In a toy model approach, we consider a superposition of two ingoing solutions and observe the probability density and probability current. We explicitly demonstrate a non-vanishing quantum backflow in a small region around the event horizon. This is in contrast to the classical black hole picture, that once an excitation crosses the horizon, it is lost forever from the outside world. Deeper implications of this phenomenon are speculated. We also study quantum backflow for another spacetime with a horizon, the Rindler spacetime, where the phenomenon can be studied only within the Rindler wedge.