Killing Invariants: An approach to the sub-classification of geometries with symmetry

Killing Invariants: An approach to the sub-classification of geometries with symmetry | 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 Killing Invariants: An approach to the sub-classification of geometries with symmetry Christian Brown, Matthew Gorban, William Julius, Ramesh Radhakrishnan, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3899523/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 10 Aug, 2024 Read the published version in General Relativity and Gravitation → Version 1 posted 7 You are reading this latest preprint version Abstract In principle, the local classification of spacetimes is always possible using the Cartan-Karlhede algorithm. However, in practice, the process of determining equivalence of two spacetimes is potentially computationally difficult or not at all possible. This difficulty will arise whenever the classifying invariants are either high-degree rational functions or depend on transcendental functions without standard inverses. In the case that spacetimes admit Killing vectors with non-trivial orbits, we propose a new set of invariant quantities, called Killing invariants. These invariants will allow for the sub-classification of spacetimes admitting the same group of symmetries and will, in principle, be substantially less complicated than any other known set. We apply this approach to the class of static spherically symmetric geometries as an illustrative example. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 10 Aug, 2024 Read the published version in General Relativity and Gravitation → Version 1 posted Editorial decision: Revision requested 21 Jun, 2024 Reviews received at journal 21 Jun, 2024 Reviewers agreed at journal 09 Feb, 2024 Reviewers invited by journal 09 Feb, 2024 Submission checks completed at journal 27 Jan, 2024 Editor assigned by journal 27 Jan, 2024 First submitted to journal 26 Jan, 2024 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. 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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-3899523","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":269579608,"identity":"bbaa9257-0e1a-40fb-9a7f-352ff056d50d","order_by":0,"name":"Christian Brown","email":"","orcid":"","institution":"Baylor University","correspondingAuthor":false,"prefix":"","firstName":"Christian","middleName":"","lastName":"Brown","suffix":""},{"id":269579610,"identity":"00488c08-81cf-4b2b-82a2-642c6b1caf32","order_by":1,"name":"Matthew Gorban","email":"","orcid":"","institution":"Baylor University","correspondingAuthor":false,"prefix":"","firstName":"Matthew","middleName":"","lastName":"Gorban","suffix":""},{"id":269579612,"identity":"0dc3a552-ba2d-4c03-a3f4-3679f75b37c4","order_by":2,"name":"William Julius","email":"","orcid":"","institution":"Baylor University","correspondingAuthor":false,"prefix":"","firstName":"William","middleName":"","lastName":"Julius","suffix":""},{"id":269579614,"identity":"c3c501db-26f5-4f4d-9e05-d88e229f2f26","order_by":3,"name":"Ramesh Radhakrishnan","email":"","orcid":"","institution":"Baylor University","correspondingAuthor":false,"prefix":"","firstName":"Ramesh","middleName":"","lastName":"Radhakrishnan","suffix":""},{"id":269579616,"identity":"90e22219-a7a8-4795-a32d-d5ffabff4fee","order_by":4,"name":"Gerald Cleaver","email":"","orcid":"","institution":"Baylor University","correspondingAuthor":false,"prefix":"","firstName":"Gerald","middleName":"","lastName":"Cleaver","suffix":""},{"id":269579618,"identity":"0c4647aa-bdc5-40d0-92c5-cb28086e7ea1","order_by":5,"name":"David Duncan McNutt","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAvElEQVRIiWNgGAWjYPACZsZ+EJVQQKyGAwnMjDMbQFoMSNGy4QCIRYwW3fazx6Q//rCW3Xx+deKHBwYM8vxiB/BrMTuTlyZxICHdeNuNt5slgA4znDk7gYCWGzxmQC2HE7fdOLsBpCXB4DaxWjbPOLv5B2laNvD3biPSljM5xhZn0tKNZ9zg3WaRYCBBhF+OnzG8UWFjLdvff3bzzR8VNvL80gS0IIAEWKUEscpBgP8AKapHwSgYBaNgJAEAEVFJCC+GeVQAAAAASUVORK5CYII=","orcid":"","institution":"UiT The Arctic University of Norway","correspondingAuthor":true,"prefix":"","firstName":"David","middleName":"Duncan","lastName":"McNutt","suffix":""}],"badges":[],"createdAt":"2024-01-26 09:14:14","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3899523/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3899523/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s10714-024-03277-x","type":"published","date":"2024-08-10T15:57:16+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":62298302,"identity":"a6a56258-eee2-4665-8824-b299f1a6d862","added_by":"auto","created_at":"2024-08-12 16:11:55","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":242766,"visible":true,"origin":"","legend":"","description":"","filename":"killinginvariantletter.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3899523/v1_covered_6aa01d48-4d1e-4bda-9aa7-d1943ef187e4.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Killing Invariants: An approach to the sub-classification of geometries with symmetry","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"general-relativity-and-gravitation","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"gerg","sideBox":"Learn more about [General Relativity and Gravitation](http://link.springer.com/journal/10714)","snPcode":"10714","submissionUrl":"https://submission.nature.com/new-submission/10714/3","title":"General Relativity and Gravitation","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-3899523/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3899523/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"In principle, the local classification of spacetimes is always possible using the Cartan-Karlhede algorithm. 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