{"title":"Fundamental complement of a gravitating region","authors":"Raphael Bousso, Sami Kaya","doi":"10.1007/s10714-025-03462-6","DOIUrl":null,"url":null,"abstract":"<div><p>Any gravitating region <i>a</i> in any spacetime gives rise to a generalized entanglement wedge, the hologram <i>e</i>(<i>a</i>). Holograms exhibit properties expected of fundamental operator algebras, such as strong subadditivity, nesting, and no-cloning. But the entanglement wedge <span>\\({{\\,\\textrm{EW}\\,}}\\)</span> of an AdS boundary region <i>B</i> with commutant <span>\\({{\\bar{B}}}\\)</span> satisfies an additional condition, complementarity: <span>\\({{\\,\\textrm{EW}\\,}}(B)\\)</span> is the spacelike complement of <span>\\({{\\,\\textrm{EW}\\,}}(\\bar{B})\\)</span> in the bulk. Here we identify an analogue of the boundary commutant <span>\\({{\\bar{B}}}\\)</span> in general spacetimes: given a gravitating region <i>a</i>, its <i>fundamental complement</i> <span>\\({{\\tilde{a}}}\\)</span> is the smallest wedge that contains all infinite world lines contained in the spacelike complement <span>\\(a'\\)</span> of <i>a</i>. We refine the definition of <i>e</i>(<i>a</i>) by requiring that it be spacelike to <span>\\({{\\tilde{a}}}\\)</span>. We prove that <i>e</i>(<i>a</i>) is the spacelike complement of <span>\\(e({{\\tilde{a}}})\\)</span> when the latter is computed in <span>\\(a'\\)</span>. We exhibit many examples of <span>\\({{\\tilde{a}}}\\)</span> and of <i>e</i>(<i>a</i>) in de Sitter, flat, and cosmological spacetimes. We find that a Big Bang cosmology (spatially closed or not) is trivially reconstructible: the whole universe is the entanglement wedge of any wedge inside it. But de Sitter space is not trivially reconstructible, despite being closed. We recover the AdS/CFT prescription by proving that <span>\\({{\\,\\textrm{EW}\\,}}(B)=e(\\)</span>causal wedge of <i>B</i>).</p></div>","PeriodicalId":578,"journal":{"name":"General Relativity and Gravitation","volume":"57 8","pages":""},"PeriodicalIF":2.8000,"publicationDate":"2025-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"General Relativity and Gravitation","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s10714-025-03462-6","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ASTRONOMY & ASTROPHYSICS","Score":null,"Total":0}
引用次数: 0
Abstract
Any gravitating region a in any spacetime gives rise to a generalized entanglement wedge, the hologram e(a). Holograms exhibit properties expected of fundamental operator algebras, such as strong subadditivity, nesting, and no-cloning. But the entanglement wedge \({{\,\textrm{EW}\,}}\) of an AdS boundary region B with commutant \({{\bar{B}}}\) satisfies an additional condition, complementarity: \({{\,\textrm{EW}\,}}(B)\) is the spacelike complement of \({{\,\textrm{EW}\,}}(\bar{B})\) in the bulk. Here we identify an analogue of the boundary commutant \({{\bar{B}}}\) in general spacetimes: given a gravitating region a, its fundamental complement\({{\tilde{a}}}\) is the smallest wedge that contains all infinite world lines contained in the spacelike complement \(a'\) of a. We refine the definition of e(a) by requiring that it be spacelike to \({{\tilde{a}}}\). We prove that e(a) is the spacelike complement of \(e({{\tilde{a}}})\) when the latter is computed in \(a'\). We exhibit many examples of \({{\tilde{a}}}\) and of e(a) in de Sitter, flat, and cosmological spacetimes. We find that a Big Bang cosmology (spatially closed or not) is trivially reconstructible: the whole universe is the entanglement wedge of any wedge inside it. But de Sitter space is not trivially reconstructible, despite being closed. We recover the AdS/CFT prescription by proving that \({{\,\textrm{EW}\,}}(B)=e(\)causal wedge of B).
期刊介绍:
General Relativity and Gravitation is a journal devoted to all aspects of modern gravitational science, and published under the auspices of the International Society on General Relativity and Gravitation.
It welcomes in particular original articles on the following topics of current research:
Analytical general relativity, including its interface with geometrical analysis
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Relativistic astrophysics
Gravitational waves: data analysis, astrophysical sources and detector science
Extensions of general relativity
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Gravitational aspects of string theory and its extensions
Quantum gravity: canonical approaches, in particular loop quantum gravity, and path integral approaches, in particular spin foams, Regge calculus and dynamical triangulations
Quantum field theory in curved spacetime
Non-commutative geometry and gravitation
Experimental gravity, in particular tests of general relativity
The journal publishes articles on all theoretical and experimental aspects of modern general relativity and gravitation, as well as book reviews and historical articles of special interest.