Quantum-Corrected Evaporation and Absorption Cross-Section of Near-Extremal Rotating Black Holes

Abstract

We revisit the Hawking evaporation history of low-temperature rotating black holes by taking into consideration the strong quantum fluctuations known to be present in the near-horizon, near-$\mathrm{AdS_2}$ throat region governed by an effective action that includes Schwarzian and two gauge modes. Imposing compatibility of this quantum framework with the semiclassical results creates a novel link between the particle angular momentum and the black hole electric charge before and after emission, leading to a nontrivial interplay between the superradiance effect and other channels. We evaluate single scalar (neutral and charged) emission of Kerr-Newman and single and di-particle emission of photons, gravitons and spinors in the Kerr spacetime. We uncover that quantum corrections may affect late time evaporation rates, which further slows down the whole evaporation process because of the near-balance between the $s$-wave channel and the superradiance channel. Specifically, we find energy decay of the form $E(t)\sim t^{-8/21}$ for scalar emission of a small, slowly rotating and charged black hole which differs from the analogous spherically symmetric quantum correction of $E(t)\sim t^{-2/5}$ already suppressed with respect to the semiclassical rate of $E(t)\sim t^{-1}$. We also discuss the quantum cross section for rotating black holes and point out various new features.

Figures (14)

• Figure 1: Schematic depiction of the black hole absorption process leading to Hawking radiation as spontaneous emission. We emphasize the role of quantum fluctuations in the throat region in green.
• Figure 2: Emission rate for the channel $l=m=0$.
• Figure 3: Emission rate for the channel $l=1, m=0$.
• Figure 4: Emission rate for the channel $l=2,m=0$.
• Figure 5: Emission rate for the channel $l=2,m=1$.