Reconstruction of Black Hole Islands from Hawking Radiation via the Algebraic Petz Map
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.
Related
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- Acoustic Schwarzschild-like black hole and analogous Hawking radiation in Einstein-bumblebee gravity
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BibTeX
@misc{vardian2026reconstruction,
title = {{Reconstruction of Black Hole Islands from Hawking Radiation via the Algebraic Petz Map}},
author = {Niloofar Vardian},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10769},
eprint = {2610.10769},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10769},
}
RIS
TY - UNPB
TI - Reconstruction of Black Hole Islands from Hawking Radiation via the Algebraic Petz Map
AU - Niloofar Vardian
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.10769
UR - https://arxiv.org/abs/2610.10769
AB - 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.
ER -