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

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

2000-01-31

arxiv.org/abs/gr-qc/0001102v1

Phys.Rev. D62 (2000) 044020

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

32 pages

Scientific paper

10.1103/PhysRevD.62.044020

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.

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