Evolution of Hawking mass under hypersurface-restricted expanding flows

Evolution of Hawking mass under hypersurface-restricted expanding flows | 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 Evolution of Hawking mass under hypersurface-restricted expanding flows Hollis Williams This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9073165/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 We present a numerical study of the evolution of the Hawking mass for closed nonspherical surfaces evolved under a class of expanding flows in Minkowski spacetime. Although formal monotonicity of the Hawking mass under smooth inverse mean curvature flow is well established in the Riemannian setting, comparatively little is known about the robustness of this behavior in discrete numerical implementations applied to explicitly embedded surfaces away from exact symmetry. We consider surfaces defined by small spherical harmonic perturbations of a round sphere and evolve them under an in-slice, time-flat flow analogous to inverse mean curvature flow. We examine the behaviour of the Hawking mass under the flow and find that monotonicity persists for a class of nonspherical perturbations and is robust under variations in perturbation amplitude and angular frequency. We also identify regimes in which numerical instabilities arise, highlighting practical challenges associated with extending such flows beyond simple symmetry assumptions. These results provide a concrete computational testbed for future investigations of uniformly expanding flows and quasi-local mass in more general spacetime settings. 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-9073165","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":606439669,"identity":"fb9c07c4-a1ed-4bd6-b80a-1a82a4a0d5b8","order_by":0,"name":"Hollis Williams","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABFUlEQVRIiWNgGAWjYBACAwbmxgMJDAw8fOyMDUC+TQJYOKEATDFj18LYANbCxgzWkpbAwAbSYkBAC4jBBpE+DNHCgEeLOXtjw4EHfw7LsDEzN3668ed8Hr98d+KHBwYM8vwMPMYGWLRY9hxsOJDYdhjksGbp3LbbxZJtvJslgA4znNnAY5yAzWE3EoFaGm6D/SKd23A7ccMx3g0gLQkGB3iMD+DSkvAHrKX5d86fcyAtm38Q1sIG1tImncN2AKRlG9wWrA47A/bLf7AW69y25MSZbbnbLBIMJAxnNrMVY/O+wfHmgw9//Emz52dvf3w7549dYj/z2c03f1TYyPOzN2+WwBbKuIAEjlgZBaNgFIyCUUAMAAB30WYycLoFyAAAAABJRU5ErkJggg==","orcid":"","institution":"Okinawa Institute of Science and Technology Graduate University","correspondingAuthor":true,"prefix":"","firstName":"Hollis","middleName":"","lastName":"Williams","suffix":""}],"badges":[],"createdAt":"2026-03-09 12:53:35","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9073165/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9073165/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":106804821,"identity":"c9520445-03ee-46f1-bdef-ff37a54471e5","added_by":"auto","created_at":"2026-04-13 15:12:42","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":245777,"visible":true,"origin":"","legend":"","description":"","filename":"NumericalevolutionofHawkingmass7.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9073165/v1_covered_4fb6071e-ed7f-480a-a0ae-69f06fab6e54.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Evolution of Hawking mass under hypersurface-restricted expanding flows","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"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":"","lastPublishedDoi":"10.21203/rs.3.rs-9073165/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9073165/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"We present a numerical study of the evolution of the Hawking mass for closed nonspherical surfaces evolved under a class of expanding flows in Minkowski spacetime. 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