{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T09:54:33Z","timestamp":1790762073181,"version":"4.1.0"},"reference-count":23,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2020,12,22]],"date-time":"2020-12-22T00:00:00Z","timestamp":1608595200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Funda&amp;#x00E7;&amp;#x00E3;o de Amparo &amp;#x00E0; Pesquisa do Estado de S&amp;#x00E3;o Paulo","award":["2019\/01511-5"],"award-info":[{"award-number":["2019\/01511-5"]}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["RTG Models of gravity 1620"],"award-info":[{"award-number":["RTG Models of gravity 1620"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we demonstrate that a phenomenon described as topological inflation, during which inflation occurs inside the core of topological defects, has a non\u2013topological counterpart. This appears in a simple set-up containing Einstein gravity coupled minimally to an electromagnetic field as well as a self-interacting, complex valued scalar field. The U(1) symmetry of the model is unbroken and leads to the existence of globally regular solutions, so-called boson stars, that develop a horizon for sufficiently strong gravitational coupling. We also find that the same phenomenon exists for black holes with scalar hair.<\/jats:p>","DOI":"10.3390\/sym13010002","type":"journal-article","created":{"date-parts":[[2020,12,22]],"date-time":"2020-12-22T20:39:29Z","timestamp":1608669569000},"page":"2","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Inflation inside Non-Topological Defects and Scalar Black Holes"],"prefix":"10.3390","volume":"13","author":[{"given":"Yves","family":"Brihaye","sequence":"first","affiliation":[{"name":"D\u00e9partement de Math\u00e9matique, Universit\u00e9 de Mons, Place du Parc, 7000 Mons, Belgium"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Felipe","family":"Console","sequence":"additional","affiliation":[{"name":"Instituto de F\u00edsica de S\u00e3o Carlos (IFSC), Universidade de S\u00e3o Paulo (USP), CP 369, S\u00e3o Carlos, SP 13560-970, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Betti","family":"Hartmann","sequence":"additional","affiliation":[{"name":"Instituto de F\u00edsica de S\u00e3o Carlos (IFSC), Universidade de S\u00e3o Paulo (USP), CP 369, S\u00e3o Carlos, SP 13560-970, Brazil"},{"name":"Institut f\u00fcr Physik, Carl-von-Ossietzky Universit\u00e4t Oldenburg, 26111 Oldenburg, Germany"},{"name":"Department of Physics and Earth Sciences, Jacobs University Bremen, 28759 Bremen, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,12,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1063\/1.3022513","article-title":"Introducing the black hole","volume":"24","author":"Ruffini","year":"1971","journal-title":"Phys. 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B"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1016\/S0550-3213(95)00100-X","article-title":"Gravitating monopole solutions 2","volume":"442","author":"Breitenlohner","year":"1995","journal-title":"Nucl. Phys. B"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Bl\u00e1zquez-Salcedo, J.L., Kahlen, S., and Kunz, J. (2020). Critical solutions in scalarized black holes. arXiv.","DOI":"10.3390\/sym12122057"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"3137","DOI":"10.1103\/PhysRevLett.72.3137","article-title":"Topological inflation","volume":"72","author":"Vilenkin","year":"1994","journal-title":"Phys. Rev. Lett."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1016\/0370-2693(94)90719-6","article-title":"Monopoles as big as a universe","volume":"327","author":"Linde","year":"1994","journal-title":"Phys. Lett. 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