Stochastically Fluctuating Black-Hole Geometry, Hawking Radiation and the Trans-Planckian Problem

TL;DR

This paper investigates how stochastic fluctuations in black hole geometry affect the propagation of massless fields and Hawking radiation, suggesting that these fluctuations could explain features of models addressing the trans-Planckian problem.

Contribution

It introduces a statistical ensemble model of black hole metric fluctuations and analyzes their impact on field propagation and Hawking radiation, linking them to modified dispersion relation models.

Findings

Backward wave packets are dissipated at high frequencies due to fluctuations.

Hawking radiation's asymptotic properties remain largely unaffected.

Fluctuations induce a critical length scale influencing wave packet propagation.

Abstract

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.