Minimal length uncertainty principle and the trans-Planckian problem of black hole physics - art. no. 044005

The minimal length uncertainty principle of Kemf, Mangano and Mann (KMM), a s derived from a mutilated quantum commutator between coordinate and moment um, is applied to describe the modes and wave packets of Hawking particles evaporated from a black hole. The trans-Planckian problem is successfully c onfronted in that the Hawking particle no longer hugs the horizon at arbitr arily close distances. Rather the mode of Schwarzschild frequency omega dev iates from the conventional trajectory when the coordinate r is given by \r -2M\similar or equal to beta(H)omega/2 pi in units of the nonlocal distance legislated into the uncertainty relation. Wave packets straddle the horizo n and spread out to fill the whole nonlocal region. The charge carried by t he packet (in the sense of the amount of ''stuff'' carried by the Klein-Gor don field) is not conserved in the non-local region and rapidly decreases t o zero as time decreases. Read in the forward temporal direction, the non-l ocal 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 mutilate d commutator has been proposed to describe an effective theory of high mome ntum scattering of zero mass modes. It is here interpreted in terms of diss ipation 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 e xtending over the nonlocal region. [S0556-2821(99)05402-8].