Metric Fluctuation Corrections to Hawking Radiation

TL;DR

This paper investigates how classical black hole geometry fluctuations influence Hawking radiation, revealing modifications in energy flux and spectrum that suggest quantum effects could alter black hole radiation properties.

Contribution

It introduces a model for black hole fluctuations affecting Hawking radiation, providing analytical corrections to flux and spectrum without full quantum treatment.

Findings

Energy flux fluctuates with amplitude and frequency of metric fluctuations.

Average energy flux is increased by two positive contributions, including a surface gravity renormalization.

Asymptotic spectrum gains thermal terms with a frequency-dependent chemical potential.

Abstract

We study how fluctuations of the black hole geometry affect the properties of Hawking radiation. Even though we treat the fluctuations classically, we believe that the results so obtained indicate what might be the effects induced by quantum fluctuations in a self consistent treatment. To characterize the fluctuations, we use the model introduced by York in which they are described by an advanced Vaidya metric with a fluctuating mass. Under the assumption of spherical symmetry, we solve the equation of null outgoing rays. Then, by neglecting the greybody factor, we calculate the late time corrections to the s-wave contributions of the energy flux and the asymptotic spectrum. We find three kind of modifications. Firstly, the energy flux fluctuates around its average value with amplitudes and frequencies determined by those of the metric fluctuations. Secondly, this average value receives two positive contributions one of which can be reinterpreted as due to the `renormalisation' of the surface gravity induced by the metric fluctuations. Finally, the asymptotic spectrum is modified by the addition of terms containing thermal factors in which the frequency of the metric fluctuations acts as a chemical potential.