Quantum Minimal Length and Transplanckian Photons

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.

25 pages, 7 figures

References in corpus (8)

• Minimal Length Uncertainty Relation and Ultraviolet Regularisation
• Entropy of Three-Dimensional Black Holes in String Theory
• Mimimal Length Uncertainty Principle and the Transplanckian Problem of Black Hole Physics
• Quantization of AdS_3 Black Holes in External Fields
• (2+1) dimensional stars
• Emission of Fermions from BTZ Black Holes
• Quantum Scalar Field on the Massless (2+1)-Dimensional Black Hole Background
• Probing the BTZ black hole with test fields

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