Mimimal Length Uncertainty Principle and the Transplanckian Problem of Black Hole Physics

Details Mimimal Length Uncertainty Principle and the Transplanckian Problem of Black Hole Physics Mimimal Length Uncertainty Principle and the Transplanckian Problem of Black Hole Physics

1998-07-09

arxiv.org/abs/hep-th/9807063v1

Phys.Rev. D59 (1999) 044005

Physics

High Energy Physics

High Energy Physics - Theory

12 pages (LateX), 1 figure

Scientific paper

10.1103/PhysRevD.59.044005

The minimal length uncertainty principle of Kempf, Mangano and Mann (KMM), as derived from a mutilated quantum commutator between coordinate and momentum, is applied to describe the modes and wave packets of Hawking particles evaporated from a black hole. The transplanckian problem is successfully confronted in that the Hawking particle no longer hugs the horizon at arbitrarily close distances. Rather the mode of Schwarzschild frequency $\omega$ deviates from the conventional trajectory when the coordinate $r$ is given by $| r - 2M|\simeq \beta_H \omega / 2 \pi$ in units of the non local distance legislated into the uncertainty relation. Wave packets straddle the horizon and spread out to fill the whole non local region. The charge carried by the packet (in the sense of the amount of "stuff" carried by the Klein--Gordon field) is not conserved in the non--local region and rapidly decreases to zero as time decreases. Read in the forward temporal direction, the non--local region thus is the seat of production of the Hawking particle and its partner. The KMM model was inspired by string theory for which the mutilated commutator has been proposed to describe an effective theory of high momentum scattering of zero mass modes. It is here interpreted in terms of dissipation which gives rise to the Hawking particle into a reservoir of other modes (of as yet unknown origin). On this basis it is conjectured that the Bekenstein--Hawking entropy finds its origin in the fluctuations of fields extending over the non local region.

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