Abstract
Quantum backflow, discovered quite a few years back, is a generic purely quantum phenomenon, in which the probability of finding a particle in a direction is nonzero (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 quantum backflow 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 nonvanishing quantum back flow 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 horizon, the Rindler spacetime, where the phenomenon can be studied only within the Rindler wedge.
Highlights
Consider a particle moving along, say, the x axis having with certainty a positive velocity along the right-hand direction with respect to some arbitrary origin x 1⁄4 0
quantum backflow (QBF) across a black hole (BH) horizon assumes significance, leading to open questions: can the backflow be directly interpreted as particles or at least can it transfer information across the horizon from the inside in some form of correlation between the ingoing wave and its QBF component? we will revisit this issue at the concluding section, we address a point that is bound to come up, i.e., is there any connection between QBF and the celebrated Hawking effect, leading to Hawking radiation
In the present work we clearly demonstrate that it is possible to have QBF from a black hole horizon but we refrain from making quantitative predictions
Summary
In classical general relativity, nothing can come out of the region behind the event horizon of a BH (that surrounds the spacetime singularity) and reach an observer at a large distance This idea was overthrown in a quantum framework whereby BHs can emit Hawking radiation which carries information about the mass, charge, and angular momentum of the BH. In [33,34], physical boundary conditions for the quantum particle wave equation at BH horizon reveal exponentially damped or enhanced solutions suggesting that particles instead of crossing the BH horizon are absorbed or reflected by it In this perspective, QBF across a BH horizon assumes significance, leading to open questions: can the backflow be directly interpreted as particles or at least can it transfer information across the horizon from the inside in some form of correlation between the ingoing wave and its QBF component? An Appendix is provided at the end showing some intermediate computational steps
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