Bulk reconstruction and non-isometry in the backwards-forwards holographic black hole map

Oliver DeWolfe (Department of Physics and Center for Theory of Quantum Matter, 390 UCB University of Colorado Boulder, Boulder, CO, 80309, USA) ; Kenneth Higginbotham (Department of Physics and Center for Theory of Quantum Matter, 390 UCB University of Colorado Boulder, Boulder, CO, 80309, USA)

The backwards-forwards map, introduced as a generalization of the non-isometric holographic maps of the black hole interior of Akers, Engelhardt, Harlow, Penington, and Vardhan to include non-trivial dynamics in the effective description, has two possible formulations differing in when the post-selection is performed. While these two forms are equivalent on the set of dynamically generated states — states formed from unitary time evolution acting on well-defined initial configurations of infalling matter — they differ on the generic set of states necessary to describe the apparent world of the infalling observer. We show that while both versions successfully reproduce the Page curve, the version involving post-selection as the final step, dubbed the backwards-forwards-post-selection (BFP) map, has the desirable properties of being non-isometric but isometric on average and providing state-dependent reconstruction of bulk operators, while the other version does not. Thus the BFP map is a suitable non-isometric code describing the black hole interior including interior interactions.

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      "value": "The backwards-forwards map, introduced as a generalization of the non-isometric holographic maps of the black hole interior of Akers, Engelhardt, Harlow, Penington, and Vardhan to include non-trivial dynamics in the effective description, has two possible formulations differing in when the post-selection is performed. While these two forms are equivalent on the set of dynamically generated states \u2014 states formed from unitary time evolution acting on well-defined initial configurations of infalling matter \u2014 they differ on the generic set of states necessary to describe the apparent world of the infalling observer. We show that while both versions successfully reproduce the Page curve, the version involving post-selection as the final step, dubbed the backwards-forwards-post-selection (BFP) map, has the desirable properties of being non-isometric but isometric on average and providing state-dependent reconstruction of bulk operators, while the other version does not. Thus the BFP map is a suitable non-isometric code describing the black hole interior including interior interactions."
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Published on:
19 June 2024
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2024 (2024)
Issue 6
Pages 1-36
DOI:
https://doi.org/10.1007/JHEP06(2024)126
arXiv:
2311.12921
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

Fulltext files: