Stochastically fluctuating black-hole geometry, Hawking radiation, and thetrans-Planckian problem - art. no. 044020

We study the propagation of null rays and massless fields in a black hole f luctuating geometry. The: metric fluctuations are induced by a small oscill ating incoming flux of energy. The flux also induces black hole mass oscill ations around its average value. We assume that the metric fluctuations are described by a statistical ensemble. The stochastic variables are the phas es and the amplitudes of Fourier modes of the fluctuations. By averaging ov er these variables, we obtain an effective propagation for massless fields which is characterized by a critical length defined by the amplitude of the metric fluctuations: Smooth wave packets with respect to this length are n ot significantly affected when they an propagated forward in time. Concomit antly, we find that the asymptotic properties of Hawking radiation are not severely modified. However, backward propagated wave packets are dissipated by the metric fluctuations once their blueshifted frequency reaches the in verse critical length. All these properties bear many resemblances with tho se obtained in models for black hole radiation based on a modified dispersi on relation. This strongly suggests that the physical origin of these model s, which were introduced to confront the trans-Planckian problem, comes fro m the fluctuations of the black hole geometry.