The scrambling power of gravity in black hole radiation

TL;DR

The work tackles the black hole information paradox through the soft-hair paradigm, embedding soft degrees of freedom into unitary QED evolution during collapse to a Reissner–Nordström black hole and quantifying information scrambling with the tripartite mutual information $I_3(A:C:D)$. It builds a framework around the Choi state of the real unitary $U_{\rm real}$ that blends Bogoliubov transformations from spacetime collapse with QED interactions, enabling a decomposition of scrambling into gravitational background, QED, and cross-term effects. The authors derive leading-order estimates showing that soft degrees of freedom drive scrambling of information initially carried by hard degrees of freedom, with $I_{3(2)}^{1} \approx -2\pi^2 (Ze^2)^2 A_1 (2\pi)^3 \frac{T}{m^2 V}$ and smaller gravitational corrections; scrambling thus persists even when QED interactions are turned off, due to vacuum non-uniqueness in collapsing spacetime. The results have implications for the soft-hair resolution of the paradox, suggest extensions to soft gravitons, and propose a picture in which scrambling evolves with the gravitational background and could, in principle, be restored after complete black hole evaporation.

Abstract

The black hole information paradox remains a profound challenge in theoretical physics. Among the proposed resolutions, the soft-hair approach stands out for its independence from any specific quantum gravity model. In this paper, we investigate how the inclusion of soft degrees of freedom in the unitary evolution of quantum electrodynamics, within a spacetime collapsing into a Reissner-Nordstrom black hole, leads to information scrambling. By evaluating the tripartite mutual information of this unitary evolution, we estimate the degree of information scrambling in the corresponding quantum channel. Our results show that the presence of soft degrees of freedom induces scrambling of information initially encoded in hard degrees of freedom, driven by quantum electrodynamics interactions and the nontrivial transformations arising from the non-uniqueness of the vacuum in the collapsing spacetime. This lays the groundwork for a deeper understanding of the black hole information paradox, particularly the mechanisms behind information scrambling.

Figures (1)

• Figure 1: The degrees of freedom in the shaded region, originally labeled $D$, $E$, and $F$, are inaccessible to an observer in the asymptotically flat region. To reflect this inaccessibility and to maintain consistency with the flat-spacetime case, we group them together and relabel the whole as $D$.