Towards bulk metric reconstruction from extremal area variations
Abstract
The Ryu–Takayanagi and Hubeny–Rangamani–Takayanagi formulae suggest that bulk geometry emerges from the entanglement structure of the boundary theory. Using these formulae, we build on a result of Alexakis, Balehowsky, and Nachman to show that in four bulk dimensions, the entanglement entropies of boundary regions of disk topology uniquely fix the bulk metric in any region foliated by the corresponding HRT surfaces. More generally, for a bulk of any dimension d ⩾ 4, knowledge of the (variations of the) areas of two-dimensional boundary-anchored extremal surfaces of disk topology uniquely fixes the bulk metric wherever these surfaces reach. This result is covariant and not reliant on any symmetry assumptions; its applicability thus includes regions of strong dynamical gravity such as the early-time interior of black holes formed from collapse. While we only show uniqueness of the metric, the approach we present provides a clear path towards an explicitspacetime metric reconstruction.
Additional Information
© 2019 IOP Publishing Ltd. Received 23 April 2019; Accepted 31 July 2019; Accepted Manuscript online 31 July 2019; Published 20 August 2019. We thank Spyridon Alexakis, Xi Dong, Netta Engelhardt, Nikolaos Eptaminitakis, Daniel Harlow, Gary Horowitz, Robin Graham, Daniel Kabat, Sorin Mardare, Reed Meyerson, and Matteo Santacesaria for useful and interesting conversations while this work was being completed; we are especially grateful to Tracey Balehowsky for her patience in explaining her work [48] to us and to Gunther Uhlmann for extensive discussions regarding inverse boundary value problems. CC would also like to thank Gunther Uhlmann for his helpful suggestions and his hospitality during the visits to the University of Washington. This research was supported in part by the National Science Foundation under Grant No. NSF PHY-1748958; in particular, NB, SF, and CK would like to thank both the KITP and OIST for hospitality during the completion of a portion of this work. NB is supported by the National Science Foundation under Grant No. 82248-13067-44-PHPXH, by the Department of Energy under Grant No. DE-SC0019380, and by New York State Urban Development Corporation Empire State Development contract no. AA289. CC acknowledges the support by the US Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632, as well as by the US Department of Defense and NIST through the Hartree Postdoctoral Fellowship at QuICS. SF acknowledges the support of the Natural Sciences and Engineering Research Council of Canada (NSERC), funding reference number SAPIN/00032-2015. The work of CK is supported by the US Department of Energy under Grant No. DE-SC0019470. This work was supported in part by a grant from the Simons Foundation (385602, AM).Attached Files
Submitted - 1904.04834.pdf
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Additional details
- Eprint ID
- 98040
- Resolver ID
- CaltechAUTHORS:20190820-131613485
- PHY-1748958
- NSF
- 82248-13067-44-PHPXH
- NSF
- DE-SC0019380
- Department of Energy (DOE)
- AA289
- New York State Urban Development Corporation Empire State Development
- DE-SC0011632
- Department of Energy (DOE)
- Department of Defense
- National Institute of Standards and Technology (NIST)
- SAPIN/00032-2015
- Natural Sciences and Engineering Research Council of Canada (NSERC)
- DE-SC0019470
- Department of Energy (DOE)
- 385602
- Simons Foundation
- Created
-
2019-08-20Created from EPrint's datestamp field
- Updated
-
2022-07-12Created from EPrint's last_modified field
- Caltech groups
- Walter Burke Institute for Theoretical Physics