Year: 2026
Type: preprint
Abstract: The island proposal guarantees a unitary Page curve for evaporating black holes, implying that operators deep behind the horizon must be fully reconstructable from asymptotic Hawking radiation. However, because the interior is causally disconnected and highly dynamical, standard entanglement wedge reconstruction methods, relying on global isometries or continuous modular flow, fail to provide this mapping. We resolve this by constructing a protocol for island reconstruction using the algebraic Petz map. By using modular theory, we reflect island operators into the accessible complement, transport them to the boundary, and map them into the radiation algebra. Furthermore, we demonstrate that this purely algebraic derivation naturally yields the structure of Papadodimas-Raju mirror operators. This framework provides a rigorous operational dictionary for the island formula, proving that information trapped inside a black hole can be decoded.
Source: arXiv (Cornell University)
Author: Vardian, Niloofar
Institution: Sharif University of Technology
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221081785