Fluctuations of an evaporating black hole from back reaction of its Hawking radiation: Questioning a premise in earlier work

TL;DR

This study uses stochastic gravity to analyze quantum-induced spacetime fluctuations in evaporating black holes, revealing growth of fluctuations over time and questioning previous assumptions about horizon flux correlations.

Contribution

It applies stochastic gravity to black hole evaporation, demonstrating the growth of metric fluctuations and challenging earlier simplified models of horizon flux correlations.

Findings

Fluctuations grow significantly over the black hole's evaporation time.

Assumption of simple correlation between horizon and far-field flux fluctuations is invalid.

Horizon fluctuations may have infinite amplitude as a hypersurface.

Abstract

This paper delineates the first steps in a systematic quantitative study of the spacetime fluctuations induced by quantum fields in an evaporating black hole. We explain how the stochastic gravity formalism can be a useful tool for that purpose within a low-energy effective field theory approach to quantum gravity. As an explicit example we apply it to the study of the spherically-symmetric sector of metric perturbations around an evaporating black hole background geometry. For macroscopic black holes we find that those fluctuations grow and eventually become important when considering sufficiently long periods of time (of the order of the evaporation time), but well before the Planckian regime is reached. In addition, the assumption of a simple correlation between the fluctuations of the energy flux crossing the horizon and far from it, which was made in earlier work on spherically-symmetric induced fluctuations, is carefully analyzed and found to be invalid. Our analysis suggests the existence of an infinite amplitude for the fluctuations of the horizon as a three-dimensional hypersurface. We emphasize the need for understanding and designing operational ways of probing quantum metric fluctuations near the horizon and extracting physically meaningful information.