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.Comment: 25 pages, LaTeX, with 3 figures, uses eps
