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This paper delineates the first steps in a systematic quantitative study ofthe spacetime fluctuations induced by quantum fields in an evaporating blackhole. We explain how the stochastic gravity formalism can be a useful tool forthat purpose within a low-energy effective field theory approach to quantumgravity. As an explicit example we apply it to the study of thespherically-symmetric sector of metric perturbations around an evaporatingblack hole background geometry. For macroscopic black holes we find that thosefluctuations grow and eventually become important when considering sufficientlylong periods of time (of the order of the evaporation time), but well beforethe Planckian regime is reached. In addition, the assumption of a simplecorrelation between the fluctuations of the energy flux crossing the horizonand far from it, which was made in earlier work on spherically-symmetricinduced fluctuations, is carefully analyzed and found to be invalid. Ouranalysis suggests the existence of an infinite amplitude for the fluctuationsof the horizon as a three-dimensional hypersurface. We emphasize the need forunderstanding and designing operational ways of probing quantum metricfluctuations near the horizon and extracting physically meaningful information.Comment: 10 pages, REVTeX; minor changes, a few references added and a brief  discussion of their relevance included. To appear in the proceedings of the  10th Peyresq meeting. Dedicated to Rafael Sorkin on the occasion of his 60th  birthda

Fluctuations of an Evaporating Black Hole from Back Reaction of Its Hawking Radiation: Questioning a Premise in Earlier Work