Charged Proca Stars

Charged Proca Stars | 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PDF Research Article Charged Proca Stars Jorge Yahir Mio Pacherre, Miguel Alcubierre Moya This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7376347/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 08 Nov, 2025 Read the published version in General Relativity and Gravitation → Version 1 posted 9 You are reading this latest preprint version Abstract We consider self-gravitating stationary configurations of a charged massive complex Proca field, also known as "charged Proca stars", in the particular case of spherical symmetry. We first present a general 3+1 decomposition of the Einstein-Maxwell-Proca system, starting from the action and field equations. We then restrict our system to the case of spherical symmetry and, after imposing a harmonic time dependence ansatz for the Proca field, we construct families of charged Proca stars for different values of the charge parameter $q$, and different values of the central Proca scalar potential $\varphi$. In a similar way to the case of scalar boson stars, one can define a critical charge $q=q_c$ that corresponds to the value for which the Coulomb repulsion of the charged Proca field exactly cancels their newtonian gravitational attraction. Just as in the case of boson stars studied in Pugliese et al. (2013) and López et al (2023), we find that supercritical solutions can exist for a limited range of charges above the critical value $q>q_c$. We also consider the binding energy $E_B$ for the different families of solutions, and find that gravitationally bound solutions such that $E_B<0$ can only exist for subcritical charges such that $q < q_c $indicating that our supercritical solutions are probably dynamically unstable against perturbations. PACS numbers: 04.20.Ex, 04.25.Dm, 95.30.Sf Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 08 Nov, 2025 Read the published version in General Relativity and Gravitation → Version 1 posted Editorial decision: Revision requested 29 Sep, 2025 Reviews received at journal 28 Sep, 2025 Reviews received at journal 26 Aug, 2025 Reviewers agreed at journal 21 Aug, 2025 Reviewers agreed at journal 20 Aug, 2025 Reviewers invited by journal 20 Aug, 2025 Editor assigned by journal 18 Aug, 2025 Submission checks completed at journal 18 Aug, 2025 First submitted to journal 14 Aug, 2025 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-7376347","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":505922120,"identity":"3f98f804-badb-439f-b807-ae7e5aa802e5","order_by":0,"name":"Jorge Yahir Mio Pacherre","email":"data:image/png;base64,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","orcid":"","institution":"National Autonomous University of Mexico","correspondingAuthor":true,"prefix":"","firstName":"Jorge","middleName":"Yahir Mio","lastName":"Pacherre","suffix":""},{"id":505922122,"identity":"7e647eb3-d307-433a-b014-a07a256765af","order_by":1,"name":"Miguel Alcubierre Moya","email":"","orcid":"","institution":"National Autonomous University of Mexico","correspondingAuthor":false,"prefix":"","firstName":"Miguel","middleName":"Alcubierre","lastName":"Moya","suffix":""}],"badges":[],"createdAt":"2025-08-14 18:38:21","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7376347/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7376347/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s10714-025-03492-0","type":"published","date":"2025-11-08T15:57:17+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":95563983,"identity":"50af64bd-715d-4178-88dc-9eb1bbda91d8","added_by":"auto","created_at":"2025-11-10 16:06:01","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":891435,"visible":true,"origin":"","legend":"","description":"","filename":"chargedProcastars.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7376347/v1_covered_20c86911-8a4b-4287-b3ad-119c154c86a9.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Charged Proca Stars","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-7376347/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7376347/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWe consider self-gravitating stationary configurations of a charged massive complex Proca field, also known as \"charged Proca stars\", in the particular case of spherical symmetry. We first present a general 3+1 decomposition of the Einstein-Maxwell-Proca system, starting from the action and field equations. \u0026nbsp;We then restrict our system to the case of spherical symmetry and, after imposing a harmonic time dependence ansatz for the Proca field, we construct families of charged Proca stars for different values of the charge parameter $q$, and different values of the central Proca scalar potential $\\varphi$. In a similar way to the case of scalar boson stars, one can define a critical charge $q=q_c$ that corresponds to the value for which the Coulomb repulsion of the charged Proca field exactly cancels their newtonian gravitational attraction. Just as in the case of boson stars studied in Pugliese et al. (2013) and López et al (2023), we find that \u0026nbsp;supercritical solutions can exist for a limited range of charges above the critical value $q\u0026gt;q_c$. \u0026nbsp;We also consider the binding energy $E_B$ for the different families of solutions, and find that gravitationally bound solutions such that $E_B\u0026lt;0$ can only exist for subcritical charges such that $q \u0026lt; q_c $indicating that our supercritical solutions are probably dynamically unstable against perturbations.\u003c/p\u003e\n\u003cp\u003ePACS numbers: 04.20.Ex, 04.25.Dm, 95.30.Sf\u003c/p\u003e","manuscriptTitle":"Charged Proca Stars","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-08-29 07:34:49","doi":"10.21203/rs.3.rs-7376347/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-09-29T07:52:59+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-09-28T21:04:34+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-08-26T15:04:03+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"19825536868547589979741645615215730571","date":"2025-08-21T09:22:36+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"296615185549304673988414209871768055669","date":"2025-08-20T20:49:33+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-08-20T13:39:43+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-08-18T15:11:56+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-08-18T15:11:33+00:00","index":"","fulltext":""},{"type":"submitted","content":"General Relativity and Gravitation","date":"2025-08-14T18:32:58+00:00","index":"","fulltext":""}],"status":"published","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}}],"origin":"","ownerIdentity":"6a66a73f-6452-4cb7-a0b8-54d455c2516d","owner":[],"postedDate":"August 29th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-11-10T16:00:08+00:00","versionOfRecord":{"articleIdentity":"rs-7376347","link":"https://doi.org/10.1007/s10714-025-03492-0","journal":{"identity":"general-relativity-and-gravitation","isVorOnly":false,"title":"General Relativity and Gravitation"},"publishedOn":"2025-11-08 15:57:17","publishedOnDateReadable":"November 8th, 2025"},"versionCreatedAt":"2025-08-29 07:34:49","video":"","vorDoi":"10.1007/s10714-025-03492-0","vorDoiUrl":"https://doi.org/10.1007/s10714-025-03492-0","workflowStages":[]},"version":"v1","identity":"rs-7376347","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7376347","identity":"rs-7376347","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}