Black Holes in the MMA–DMF Framework: Resolving the Information and Entropy Paradoxes

Black Holes in the MMA–DMF Framework: Resolving the Information and Entropy Paradoxes | 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 Black Holes in the MMA–DMF Framework: Resolving the Information and Entropy Paradoxes Paulo Adriano This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8622775/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 MMA–DMF framework modifies gravity by adding a single geometric scalar degree of freedom with a characteristic energy scale of order 100 TeV. In this work we assemble the black–hole sector of MMA–DMF and show how it leads to a concrete, testable resolution of both the entropy and information paradoxes. Starting from a static, spherically symmetric regular metric with a de Sitter core, we derive the thermodynamic quantities of MMA–DMF black holes, including a corrected entropy SMMA–DMF(A), a modified evaporation law with a finite remnant mass, and a self–consistent Page curve in which the black–hole entropy decreases while the radiation entropy increases, saturates and eventually falls. We then systematise strong–gravity and information tests: neutron–star and Super–TOV configurations; intermediate–mass and microscopic black holes; a “Sad Trombone” fast–radio–burst test; ringdown tests (including scalar breathing modes and quasinormal–mode deviations), shadow and photon–ring tests, and modified ISCO spectra. Dedicated information–paradox tests quantify deviations from Kerr, gravitational–wave echoes, and the Total Determinism Test for Black Holes (TDT–BH), relating corrected entropy, echo delays and quasinormal–mode shifts across the full mass spectrum. Using these ingredients we demonstrate that MMA–DMF black holes are free of curvature singularities, possess a finite and computable entropy at all stages of their evolution, obey a generalised second law and can preserve quantum information through regular cores, long–lived remnants and delayed echo channels, while predicting falsifiable observational signatures Theoretical Physics MMA-DMF black holes information paradox entropy paradox Hawking radiation Bekenstein– Hawking entropy Page curve gravitational–wave echoes modified gravity Full Text Additional Declarations The authors declare no competing interests. Supplementary Files BlackHolesResolvingtheInformationandEntropyParadoxestex.zip Files.zip Ancilliary Files and Latex 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-8622775","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":575869894,"identity":"e410babb-ea49-4688-b936-395eccc08ae4","order_by":0,"name":"Paulo Adriano","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAuklEQVRIiWNgGAWjYBACAxDxgeEAD2laGGeAtLBBBCSI0sLMw3CAgXgt5uzdiY9tau7ImMs3H/zAuMOmjqAWy56zm41zjj3jsWxjS5ZgPJNGhMNu5G6Tzm04zGNwjMeMgbHtMFFatv+2BGvh/wbU8p84W5gZIbawAbUcIELLmbObJXuOHQb6Jc1YIrEtWbKBoJbjvRs//Kg5bG/OfPjhh49tdvwEbUHoBREJxKuHaRkFo2AUjIJRgA0AAAQWO13tMX01AAAAAElFTkSuQmCC","orcid":"https://orcid.org/0009-0008-4646-4616","institution":"","correspondingAuthor":true,"prefix":"","firstName":"Paulo","middleName":"","lastName":"Adriano","suffix":""}],"badges":[],"createdAt":"2026-01-17 01:30:25","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-8622775/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8622775/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":100660030,"identity":"e245b2c9-7e3a-4811-a1ee-21512c452080","added_by":"auto","created_at":"2026-01-20 08:29:36","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":16521866,"visible":true,"origin":"","legend":"","description":"","filename":"BlackHolesResolvingtheInformationandEntropyParadoxes.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8622775/v1_covered_bdb23713-8474-40e8-8cfc-2ed60f63c55f.pdf"},{"id":100658086,"identity":"9c21954a-b056-4aa0-a63f-6943875e860f","added_by":"auto","created_at":"2026-01-20 08:11:23","extension":"zip","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":16520781,"visible":true,"origin":"","legend":"","description":"","filename":"BlackHolesResolvingtheInformationandEntropyParadoxestex.zip","url":"https://assets-eu.researchsquare.com/files/rs-8622775/v1/af21ce5ae2a5d4b07f4b18c5.zip"},{"id":100657741,"identity":"4bdbf91c-a15f-4e71-b690-7ad49c558b95","added_by":"auto","created_at":"2026-01-20 08:08:52","extension":"zip","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":28755512,"visible":true,"origin":"","legend":"\u003cp\u003eAncilliary Files and Latex\u003c/p\u003e","description":"","filename":"Files.zip","url":"https://assets-eu.researchsquare.com/files/rs-8622775/v1/404c7ce208c8dde7b0bee547.zip"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eBlack Holes in the MMA–DMF Framework: Resolving the Information and Entropy Paradoxes\u003c/p\u003e","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":"MMA-DMF, black holes, information paradox, entropy paradox, Hawking radiation, Bekenstein– Hawking entropy, Page curve, gravitational–wave echoes, modified gravity","lastPublishedDoi":"10.21203/rs.3.rs-8622775/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8622775/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe MMA–DMF framework modifies gravity by adding a single geometric scalar degree of freedom with a characteristic energy scale of order 100 TeV. In this work we assemble the black–hole sector of MMA–DMF and show how it leads to a concrete, testable resolution of both the entropy and information paradoxes. Starting from a static, spherically symmetric regular metric with a de Sitter core, we derive the thermodynamic quantities of MMA–DMF black holes, including a corrected entropy SMMA–DMF(A), a modified evaporation law with a finite remnant\u003c/p\u003e\n\u003cp\u003emass, and a self–consistent Page curve in which the black–hole entropy decreases while the radiation entropy increases, saturates and eventually falls. We then systematise strong–gravity and information tests: neutron–star and Super–TOV configurations; intermediate–mass and microscopic black holes; a “Sad Trombone” fast–radio–burst test; ringdown tests (including scalar breathing modes and quasinormal–mode deviations), shadow and photon–ring tests, and modified ISCO spectra. 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