Factorization of the Hilbert space of eternal black holes in general relativity

Vijay Balasubramanian; Ben Craps; Juan Hernandez; Mikhail Khramtsov; Maria Knysh

doi:https://doi.org/10.1007/JHEP01(2025)046

Factorization of the Hilbert space of eternal black holes in general relativity

Vijay Balasubramanian, Ben Craps, Juan Hernandez, Mikhail Khramtsov, Maria Knysh

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

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Abstract

We generalize recent results in two-dimensional Jackiw-Teitelboim gravity to
study factorization of the Hilbert space of eternal black holes in quantum gravity with a
negative cosmological constant in any dimension. We approach the problem by computing the
trace of two-sided observables as a sum over a recently constructed family of semiclassically
well-controlled black hole microstates. These microstates, which contain heavy matter shells
behind the horizon and form an overcomplete basis of the Hilbert space, exist in any theory
of gravity with general relativity as its low energy limit. Using this representation of the
microstates, we show that the trace of operators dual to functions of the Hamiltonians of
the left and right holographic CFTs factorizes into a product over left and right factors to
leading order in the semiclassical limit. Under certain conditions this implies factorization
of the Hilbert space.

Original language	English
Article number	46
Number of pages	32
Journal	JHEP reports
Volume	2025
Issue number	1
DOIs	https://doi.org/10.1007/JHEP01(2025)046
Publication status	Published - 8 Jan 2025

Bibliographical note

Funding Information:
We would like to thank Will Chan, Shira Chapman, Charlie Cummings, Chitraang Murdia, Martin Sasieta, Alejandro Vilar L\u00F3pez, Gabriel Wong and Tom Yildirim for useful discussions. VB was supported in part by the DOE through DE-SC0013528 and QuantISED grant DE-SC0020360, and in part by the Eastman Professorship at Balliol College, Oxford. Work at VUB was supported by FWO-Vlaanderen project G012222N and by the VUB Research Council through the Strategic Research Program High-Energy Physics. JH is supported by FWO-Vlaanderen through a Junior Postdoctoral Fellowship.

Publisher Copyright:
© The Author(s) 2025.

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https://doi.org/10.1007/JHEP01(2025)046Licence: CC BY

JHEP01(2025)046Final published version, 693 KBLicence: CC BY

Cite this

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abstract = "We generalize recent results in two-dimensional Jackiw-Teitelboim gravity tostudy factorization of the Hilbert space of eternal black holes in quantum gravity with anegative cosmological constant in any dimension. We approach the problem by computing thetrace of two-sided observables as a sum over a recently constructed family of semiclassicallywell-controlled black hole microstates. These microstates, which contain heavy matter shellsbehind the horizon and form an overcomplete basis of the Hilbert space, exist in any theoryof gravity with general relativity as its low energy limit. Using this representation of themicrostates, we show that the trace of operators dual to functions of the Hamiltonians ofthe left and right holographic CFTs factorizes into a product over left and right factors toleading order in the semiclassical limit. Under certain conditions this implies factorizationof the Hilbert space.",

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note = "Funding Information: We would like to thank Will Chan, Shira Chapman, Charlie Cummings, Chitraang Murdia, Martin Sasieta, Alejandro Vilar L\u00F3pez, Gabriel Wong and Tom Yildirim for useful discussions. VB was supported in part by the DOE through DE-SC0013528 and QuantISED grant DE-SC0020360, and in part by the Eastman Professorship at Balliol College, Oxford. Work at VUB was supported by FWO-Vlaanderen project G012222N and by the VUB Research Council through the Strategic Research Program High-Energy Physics. JH is supported by FWO-Vlaanderen through a Junior Postdoctoral Fellowship. Publisher Copyright: {\textcopyright} The Author(s) 2025.",

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N1 - Funding Information: We would like to thank Will Chan, Shira Chapman, Charlie Cummings, Chitraang Murdia, Martin Sasieta, Alejandro Vilar L\u00F3pez, Gabriel Wong and Tom Yildirim for useful discussions. VB was supported in part by the DOE through DE-SC0013528 and QuantISED grant DE-SC0020360, and in part by the Eastman Professorship at Balliol College, Oxford. Work at VUB was supported by FWO-Vlaanderen project G012222N and by the VUB Research Council through the Strategic Research Program High-Energy Physics. JH is supported by FWO-Vlaanderen through a Junior Postdoctoral Fellowship. Publisher Copyright: © The Author(s) 2025.

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N2 - We generalize recent results in two-dimensional Jackiw-Teitelboim gravity tostudy factorization of the Hilbert space of eternal black holes in quantum gravity with anegative cosmological constant in any dimension. We approach the problem by computing thetrace of two-sided observables as a sum over a recently constructed family of semiclassicallywell-controlled black hole microstates. These microstates, which contain heavy matter shellsbehind the horizon and form an overcomplete basis of the Hilbert space, exist in any theoryof gravity with general relativity as its low energy limit. Using this representation of themicrostates, we show that the trace of operators dual to functions of the Hamiltonians ofthe left and right holographic CFTs factorizes into a product over left and right factors toleading order in the semiclassical limit. Under certain conditions this implies factorizationof the Hilbert space.

AB - We generalize recent results in two-dimensional Jackiw-Teitelboim gravity tostudy factorization of the Hilbert space of eternal black holes in quantum gravity with anegative cosmological constant in any dimension. We approach the problem by computing thetrace of two-sided observables as a sum over a recently constructed family of semiclassicallywell-controlled black hole microstates. These microstates, which contain heavy matter shellsbehind the horizon and form an overcomplete basis of the Hilbert space, exist in any theoryof gravity with general relativity as its low energy limit. Using this representation of themicrostates, we show that the trace of operators dual to functions of the Hamiltonians ofthe left and right holographic CFTs factorizes into a product over left and right factors toleading order in the semiclassical limit. Under certain conditions this implies factorizationof the Hilbert space.

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Factorization of the Hilbert space of eternal black holes in general relativity

Abstract

Bibliographical note

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SRP72: SRP-Onderzoekszwaartepunt: High-energy physics (HEP@VUB).

FWOAL1051: Quantum complexity, quantum entanglement and the emergence of spacetime

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Factorization of the Hilbert space of eternal black holes in general relativity

Abstract

Bibliographical note

Access to Document

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Projects

SRP72: SRP-Onderzoekszwaartepunt: High-energy physics (HEP@VUB).

FWOAL1051: Quantum complexity, quantum entanglement and the emergence of spacetime

Cite this