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Phys."],"abstract":"<jats:title>A<jats:sc>bstract<\/jats:sc>\n          <\/jats:title>\n          <jats:p>Tidal Love numbers of anti-de Sitter black holes are understood as linear response coefficients governing how the holographically dual plasma polarizes when the geometry of the space, in which the plasma lives, is deformed. So far, this picture has been applied only to black branes with plane wave perturbations. We fill the gap in the literature by performing the computation of tidal Love numbers for the four-dimensional Schwarzschild solution in global anti-de Sitter, which is dual to a conformal plasma on <jats:italic>S<\/jats:italic>\n            <jats:sup>2<\/jats:sup>. We conclude about the effect of the bulk gravitational perturbations on the boundary metric and stress tensor, responsible for the geometric polarization. The computation of the tidal Love numbers is performed in both Regge-Wheeler gauge and the Kodama-Ishibashi gauge-invariant approach. We spell out how to convert the tidal Love numbers determined in these two formalisms and find perfect agreement. We also relate the Kodama-Ishibashi formalism with the Kovtun-Starinets approach, which is particularly well suited for the holographic analysis of black branes. This allows us to compare with the tidal Love number results for black branes in anti-de Sitter, also finding agreement in the relevant regime.<\/jats:p>","DOI":"10.1007\/jhep12(2024)224","type":"journal-article","created":{"date-parts":[[2025,1,4]],"date-time":"2025-01-04T03:49:44Z","timestamp":1735962584000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Tidal Love numbers of static black holes in anti-de Sitter"],"prefix":"10.1007","volume":"2024","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5705-5550","authenticated-orcid":false,"given":"Edgardo","family":"Franzin","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/02be6w209","id-type":"ROR","asserted-by":"publisher"}],"name":"\u201cSapienza\u201d Universit\u00e0 di Roma"},{"id":[{"id":"https:\/\/ror.org\/005ta0471","id-type":"ROR","asserted-by":"publisher"}],"name":"INFN, Sezione di Roma1"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9937-486X","authenticated-orcid":false,"given":"Antonia M.","family":"Frassino","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/004fze387","id-type":"ROR","asserted-by":"publisher"}],"name":"SISSA, International School for Advanced Studies"},{"id":[{"id":"https:\/\/ror.org\/05j3snm48","id-type":"ROR","asserted-by":"publisher"}],"name":"INFN, Sezione di Trieste"},{"id":[{"id":"https:\/\/ror.org\/04pmn0e78","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Alcal\u00e1"},{"id":[{"id":"https:\/\/ror.org\/021018s57","id-type":"ROR","asserted-by":"publisher"}],"name":"Universitat de Barcelona"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9619-7087","authenticated-orcid":false,"given":"Jorge V.","family":"Rocha","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/014837179","id-type":"ROR","asserted-by":"publisher"}],"name":"Departamento de Matem\u00e1tica, ISCTE \u2014 Instituto Universit\u00e1rio de Lisboa"},{"id":[{"id":"https:\/\/ror.org\/01c27hj86","id-type":"ROR","asserted-by":"publisher"}],"name":"Centro de Astrof\u00edsica e Gravita\u00e7\u00e3o \u2014 CENTRA, Instituto Superior T\u00e9cnico \u2014 IST, Universidade de Lisboa \u2014 UL"},{"id":[{"id":"https:\/\/ror.org\/02ht4fk33","id-type":"ROR","asserted-by":"publisher"}],"name":"Instituto de Telecomunica\u00e7\u00f5es \u2014 IUL"}]}],"member":"297","published-online":{"date-parts":[[2024,12,30]]},"reference":[{"key":"25233_CR1","doi-asserted-by":"crossref","unstructured":"T. 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