We study the propagation of null rays and massless fields in a black hole
fluctuating geometry. The metric fluctuations are induced by a small
oscillating incoming flux of energy. The flux also induces black hole mass
oscillations around its average value. We assume that the metric fluctuations
are described by a statistical ensemble. The stochastic variables are the
phases and the amplitudes of Fourier modes of the fluctuations. By averaging
over 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 not
significantly affected when they are propagated forward in time. Concomitantly,
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 blue shifted frequency reaches the inverse
critical length. All these properties bear many resemblences with those
obtained in models for black hole radiation based on a modified dispersion
relation. This strongly suggests that the physical origin of these models,
which were introduced to confront the trans-Planckian problem, comes from the
fluctuations of the black hole geometry.Comment: 32 page
