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Phys."],"abstract":"<jats:title>A<jats:sc>bstract<\/jats:sc>\n          <\/jats:title>\n          <jats:p>We add an <jats:italic>S<\/jats:italic>\n            <jats:sup>1<\/jats:sup> extra dimension (size <jats:italic>L<\/jats:italic>) to the well known <jats:italic>D<\/jats:italic> = 4 static, spherically symmetric <jats:italic>Q<\/jats:italic>-balls and boson stars. We show that the resulting <jats:italic>uniform horizonless boson strings<\/jats:italic> possess a static zero-mode for a critical value of <jats:italic>L<\/jats:italic>. This is at the threshold of a Gregory-Laflamme instability of these objects, occurring for larger values of <jats:italic>L<\/jats:italic>. The non-linear continuation of the zero-mode yields <jats:italic>D<\/jats:italic> = 5 <jats:italic>non-uniform boson strings<\/jats:italic>. In addition, there are also intrinsic <jats:italic>D<\/jats:italic> = 5 solutions describing <jats:italic>localized boson stars on the S<\/jats:italic>\n            <jats:sup>1<\/jats:sup>, supported by the contribution of the scalar field Kaluza-Klein modes. Basic properties of all three types of aforementioned solutions are discussed, together with their phase space.<\/jats:p>","DOI":"10.1007\/jhep08(2025)049","type":"journal-article","created":{"date-parts":[[2025,8,7]],"date-time":"2025-08-07T02:11:22Z","timestamp":1754532682000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Gregory-Laflamme-type instability of boson strings and related phases in D = 5 Kaluza-Klein theory"],"prefix":"10.1007","volume":"2025","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9619-2013","authenticated-orcid":false,"given":"C.","family":"Herdeiro","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00nt41z93","id-type":"ROR","asserted-by":"publisher"}],"name":"Universidade de Aveiro"},{"id":[{"id":"https:\/\/ror.org\/00nt41z93","id-type":"ROR","asserted-by":"publisher"}],"name":"Center for Research and Development in Mathematics and Applications (CIDMA)"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0503-896X","authenticated-orcid":false,"given":"E.","family":"Radu","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00nt41z93","id-type":"ROR","asserted-by":"publisher"}],"name":"Universidade de Aveiro"},{"id":[{"id":"https:\/\/ror.org\/00nt41z93","id-type":"ROR","asserted-by":"publisher"}],"name":"Center for Research and Development in Mathematics and Applications (CIDMA)"}]}],"member":"297","published-online":{"date-parts":[[2025,8,6]]},"reference":[{"key":"26908_CR1","unstructured":"Aristotle, On the heavens, translated by J.L. 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