{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T13:42:07Z","timestamp":1769002927000,"version":"3.49.0"},"reference-count":49,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,2,7]],"date-time":"2025-02-07T00:00:00Z","timestamp":1738886400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"development program of the Volga Region Mathematical Center","award":["075-02-2024-1438"],"award-info":[{"award-number":["075-02-2024-1438"]}]},{"name":"development program of the Volga Region Mathematical Center","award":["FSWU-2023-0073"],"award-info":[{"award-number":["FSWU-2023-0073"]}]},{"name":"Ministry of Science and Higher Education of the Russian Federation","award":["075-02-2024-1438"],"award-info":[{"award-number":["075-02-2024-1438"]}]},{"name":"Ministry of Science and Higher Education of the Russian Federation","award":["FSWU-2023-0073"],"award-info":[{"award-number":["FSWU-2023-0073"]}]},{"name":"Kazan Federal University Strategic Academic Leadership Program","award":["075-02-2024-1438"],"award-info":[{"award-number":["075-02-2024-1438"]}]},{"name":"Kazan Federal University Strategic Academic Leadership Program","award":["FSWU-2023-0073"],"award-info":[{"award-number":["FSWU-2023-0073"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper presents a study of brane formation in six-dimensional space. There is no a priori assumption of the existence of brane(s). However, an analysis of the generalized Einstein equations shows that there is a set of metrics describing two static branes even in the absence of matter fields. At the same time, no one-brane configurations were found. The trapping of massive particles on branes is a consequence of the metric structure, which prevents these particles from moving between branes. It is shown that communication between charged particles on different branes is provided by photons. Such positron\u2013electron annihilation could be studied experimentally at the LHC collider. The Higgs field is distributed between the branes in such a way that it can serve as a Higgs portal connecting two worlds located on different branes. The values of the 4D physical parameters depend on the extra metric structure near the branes. We also found a non-trivial effect of the decompactification of extra space during the Hubble parameter variation.<\/jats:p>","DOI":"10.3390\/sym17020252","type":"journal-article","created":{"date-parts":[[2025,2,7]],"date-time":"2025-02-07T09:02:42Z","timestamp":1738918962000},"page":"252","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Spontaneous Brane Formation"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3195-2541","authenticated-orcid":false,"given":"Arkadiy A.","family":"Popov","sequence":"first","affiliation":[{"name":"N. I. Lobachevsky Institute of Mathematics and Mechanics, Kazan Federal University, Kremlyovskaya 18, Kazan 420008, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9259-3645","authenticated-orcid":false,"given":"Sergey G.","family":"Rubin","sequence":"additional","affiliation":[{"name":"N. I. Lobachevsky Institute of Mathematics and Mechanics, Kazan Federal University, Kremlyovskaya 18, Kazan 420008, Russia"},{"name":"Moscow Engineering Physics Institute, National Research Nuclear University MEPhI, Kashirskoe Shosse 31, Moscow 115409, Russia"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,7]]},"reference":[{"key":"ref_1","first-page":"720","article-title":"Kaluza-Klein Cosmologies and Inflation","volume":"D30","author":"Abbott","year":"1984","journal-title":"Phys. Rev."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/S0370-2693(00)00874-1","article-title":"Mass hierarchy and localization of gravity in extra time","volume":"B488","author":"Chaichian","year":"2000","journal-title":"Phys. Lett."},{"key":"ref_3","first-page":"124048","article-title":"Compactifying de Sitter space naturally selects a small cosmological constant","volume":"D90","author":"Brown","year":"2014","journal-title":"Phys. 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