Quantum Cross-section of Near-extremal Black Holes

Abstract

We explore how to detect the large quantum fluctuations in the throat of a near-extremal black hole, where the dynamics are governed by the Schwarzian theory. To this end, we scatter a low-frequency wave of a massless, minimal scalar off the black hole and calculate the absorption cross-section. In the semiclassical regime, where the Schwarzian is weakly coupled, we recover the universal result that the cross-section equals the horizon area. However, in the strongly coupled regime, where quantum fluctuations dominate, we find that the absorption cross-section exceeds the semiclassical prediction. This result may seem counterintuitive, given that the density of black hole states is suppressed in this regime. Nevertheless, two effects outweigh this suppression. First, quantum fluctuations enhance absorption transitions between individual states, with the effect becoming stronger closer to the ground state. Second, these fluctuations significantly reduce stimulated emission. We conclude that a measurement showing an enhanced absorption cross-section serves as a clear signature of the large quantum fluctuations in the geometry.