Quantum Minimal Length and Transplanckian Photons

TL;DR

This paper explores the effects of a minimal length in quantum gravity on black hole evaporation, analyzing wave functions and non-locality, and suggesting implications for unitarity in quantum black hole physics.

Contribution

It introduces a new quantum theory framework with a minimal length that simplifies the wave equations for black hole evaporation and clarifies the physical relevance of solutions.

Findings

Oscillating terms are removed in the new framework.

Infinite constants are shown to have no physical meaning.

Non-locality zones depend on the energy scale.

Abstract

In this paper we first give arguments supporting the idea that a B.T.Z black hole can face a transplankian problem even when its mass is small. K.M.M quantum theory is applied to the Hawking evaporation of the Schwarzchild and B.T.Z black holes. Working in the physically safe quasi position representation, we argue that the oscillating term present in a previous analysis is removed so that actually one doesn't need an average procedure. We expand the s wave function as the exponential of a series in the minimal length of the new quantum theory. This reduces an infinite order differential equation to a numerable set of finite order ones. We obtain the striking result that the infinity of arbitrary constants induced by the order of the wave equation has no physical meaning due to normalization. We finally construct gaussian wave pacqets and study their trajectories. We suggest a quantitative description of the non locality zone and its dependance on the K.M.M energy scale. Potential incidences on unitarity are briefly evoqued.