Bi-Structured Horizon Geometry and Spectral Dimension Running at Black Hole Horizons

Bi-Structured Horizon Geometry and Spectral Dimension Running at Black Hole Horizons | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Bi-Structured Horizon Geometry and Spectral Dimension Running at Black Hole Horizons Shalender Singh, Vishnu Priya Singh Parmar This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9250599/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The black hole information paradox arises in part from an implicit identification: the metric structure governing spacetime geometry and the propagation structure governing quantum dynamics are assumed to coincide. We argue that relaxing this identification resolves the tension between the Equivalence Principle and unitarity without modifying either. Treating the event horizon as a bi-structured space carrying an intrinsic metric geometry and an independent propagation graph, we show that the spectral dimension of the horizon is not a fixed invariant but a scale-dependent observable that runs from a reduced value at short times—identified with the scrambling regime—to the classical spacetime dimension at late times. This running is consistent with dimensional reduction phenomena established in causal dynamical triangulations, asymptotically safe gravity, and Hořava–Lifshitz gravity. In this framework, the AMPS firewall corresponds to the short-time spectral regime: a scale-dependent phase associated with constrained propagation, not a curvature singularity of the metric geometry. A freely falling observer probing the horizon at macroscopic timescales traverses the smooth metric structure and perceives no drama. Unitarity is preserved because the constrained propagation is generated by a Hermitian Laplacian. We present a lattice simulation demonstrating the spectral crossover explicitly, confirming the coexistence of a low-dimensional spectral trap and a smooth macroscopic geometry within a single object. Implications for gravitational wave echoes, holographic complexity, and Swampland-type consistency criteria are discussed. Black Hole Information Paradox Matrix Models Non-Commutative Geometry Arithmetic Rigidity Holographic Emergence Spectral Dimension Firewall Paradox Scrambling Time Admissible Propagation Bi-Structured Spaces Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9250599","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":614279033,"identity":"09da3fc9-94d2-4738-a019-e133fc68c3ec","order_by":0,"name":"Shalender Singh","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA/UlEQVRIie3RMUvDQBTA8XdkyHKS9QXFfIVXOjgU6lc5yZAlBMeCYIXCudT9ip/CRRwvHNTlugfqkC8g1C1CBUOL2CU9uxW8/3bH/eAdD8DnO8YQmAYIAMI7ALG54k4CW8L1huABBMXP2UGSx0mtP14G5xez9/mqXg9vo3ChoRk9dxJ6m1M5s1n/bFmkSvAU42kh2NQuuwkKMifSXKnTvA8CA6SKU8BkN0lUtjJf0oxVbFtCY7x0EahyMkwagchbIgwSOghV+XX5ILOe4kUKQr/GyuZU7vtLO9hT/SkHCYYLw5r1TRTd217djPYM9tvOOvRf3oN76T6fz/dv+wbO5VWzx3DEbQAAAABJRU5ErkJggg==","orcid":"","institution":"","correspondingAuthor":true,"prefix":"","firstName":"Shalender","middleName":"","lastName":"Singh","suffix":""},{"id":614279034,"identity":"2eca332c-d78d-44a4-b477-5ce10d40dbbb","order_by":1,"name":"Vishnu Priya Singh Parmar","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Vishnu","middleName":"Priya Singh","lastName":"Parmar","suffix":""}],"badges":[],"createdAt":"2026-03-28 07:24:34","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9250599/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9250599/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":105777921,"identity":"5c8f2dae-3699-4863-b1ed-4feab4d1d901","added_by":"auto","created_at":"2026-03-31 03:55:37","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":610932,"visible":true,"origin":"","legend":"","description":"","filename":"eventhorizongeometryv2IJTP.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9250599/v1_covered_b2457c72-21a9-4f98-8ea3-88d506950acd.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Bi-Structured Horizon Geometry and Spectral Dimension Running at Black Hole Horizons","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Black Hole Information Paradox, Matrix Models, Non-Commutative Geometry, Arithmetic Rigidity, Holographic Emergence, Spectral Dimension, Firewall Paradox, Scrambling Time, Admissible Propagation, Bi-Structured Spaces","lastPublishedDoi":"10.21203/rs.3.rs-9250599/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9250599/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe black hole information paradox arises in part from an implicit identification: the metric structure governing spacetime geometry and the propagation structure governing quantum dynamics are assumed to coincide. 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A freely falling observer probing the horizon at macroscopic timescales traverses the smooth metric structure and perceives no drama. Unitarity is preserved because the constrained propagation is generated by a Hermitian Laplacian. We present a lattice simulation demonstrating the spectral crossover explicitly, confirming the coexistence of a low-dimensional spectral trap and a smooth macroscopic geometry within a single object. 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