Fluctuations of the Hawking Flux

TL;DR

This paper investigates the fluctuations in Hawking radiation flux from evaporating black holes, revealing large fluctuations that challenge the semiclassical gravity approximation on short time scales.

Contribution

It compares two approaches to flux fluctuations, showing how large fluctuations occur and affect the validity of semiclassical gravity near black holes.

Findings

Flux undergoes large fluctuations on the order of the black hole's mass.

Mean squared flux grows linearly over time in both approaches.

Fluctuation growth rate differs by a factor of four between the two methods.

Abstract

The fluctuations of the flux radiated by an evaporating black hole will be discussed. Two approaches to this problem will be adopted. In the first, the squared flux operator is defined by normal ordering. In this case, both the mean flux and the mean squared flux are well defined local quantites. It is shown that the flux undergoes large fluctuations on a time scale of the order of the black hole's mass. Thus the semiclassical theory of gravity, in which a classical gravitational field is coupled to the expectation value of the stress tensor, breaks down below this time scale. In the second approach, one does not attempt to give meaning to the squared flux as a local quantity, but only as a time-averaged quantity. In both approaches, the mean squared mass minus the square of the mean mass grows linearly in time, but four times as fast in the second approach as in the first.