Black Hole Interior and Quantum Error Correction with Dynamical Gravity

TL;DR

This paper explores how dynamical gravity affects the embedding of black hole interior information in Hawking radiation, showing that backreaction prevents causality violations suggested by earlier models.

Contribution

It demonstrates that including dynamical gravity and backreaction in the analysis resolves apparent causality violations in black hole information transfer.

Findings

Backreaction causes mutual information to vanish.

Dynamical gravity prevents causality violations.

Results extend previous topological models to realistic gravity scenarios.

Abstract

According to the island formula, information in the code subspace defined in the black hole interior is embedded in the Hawking radiation after the Page time. At first sight, this embedding suggests that operations acting on the Hawking radiation could modify the information in the code subspace, potentially leading to an apparent violation of causality. Indeed, in previous studies based on the PSSY model, which incorporates only the topological degrees of freedom of gravity, it was shown that when the error is sufficiently large, a violation of causality can arise, as indicated by a nonvanishing mutual information. In this paper, we investigate the situation in which dynamical gravity also acts on the Hawking radiation. In this case, operations on the Hawking radiation induce nontrivial backreaction on the bulk spacetime appearing in the gravitational path integral for the mutual information -- an effect that is absent when the Hawking radiation is non-gravitating. We find that this backreaction renders the relevant mutual information vanishing. This result implies that, in theories with dynamical gravity, the apparent violation of causality is resolved.