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Quantum Grav."],"published-print":{"date-parts":[[2026,2,28]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    We present new spherically symmetric solutions of the Einstein\u2013Klein\u2013Gordon equations in a quasi-stationary approximation that describe self-gravitating scalar field configurations around a black hole, including angular momentum number\n                    <jats:inline-formula>\n                      <jats:tex-math>\n                        \n                      <\/jats:tex-math>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mrow>\n                          <mml:mi>\u2113<\/mml:mi>\n                        <\/mml:mrow>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    . An approach analogous to the one which gives rise to\n                    <jats:inline-formula>\n                      <jats:tex-math>\n                        \n                      <\/jats:tex-math>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mrow>\n                          <mml:mi>\u2113<\/mml:mi>\n                        <\/mml:mrow>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    -boson stars is used here to construct self-gravitating \u2018gravitational atoms\u2019 with\n                    <jats:inline-formula>\n                      <jats:tex-math>\n                        \n                      <\/jats:tex-math>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mrow>\n                          <mml:mi>\u2113<\/mml:mi>\n                          <mml:mtext>\u2a7e<\/mml:mtext>\n                          <mml:mn>0<\/mml:mn>\n                        <\/mml:mrow>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    . We refer to these new solutions as\n                    <jats:italic>noble gravitational atoms<\/jats:italic>\n                    , by analogy with noble atoms, which are characterized by closed electron shells. We show that, in the proper limit, noble gravitational atoms approach\n                    <jats:inline-formula>\n                      <jats:tex-math>\n                        \n                      <\/jats:tex-math>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mrow>\n                          <mml:mi>\u2113<\/mml:mi>\n                        <\/mml:mrow>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    -boson stars globally, displaying noticeable differences only in a region very close to the event horizon. Noble gravitational atoms with\n                    <jats:inline-formula>\n                      <jats:tex-math>\n                        \n                      <\/jats:tex-math>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mrow>\n                          <mml:mi>\u2113<\/mml:mi>\n                          <mml:mo>&gt;<\/mml:mo>\n                          <mml:mn>0<\/mml:mn>\n                        <\/mml:mrow>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    sometimes present density maxima located at relatively large radii, with small density close to the horizon for\n                    <jats:inline-formula>\n                      <jats:tex-math>\n                        \n                      <\/jats:tex-math>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mrow>\n                          <mml:mi>\u2113<\/mml:mi>\n                          <mml:mo>&gt;<\/mml:mo>\n                          <mml:mn>1<\/mml:mn>\n                        <\/mml:mrow>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    . Furthermore, they do not always present the typical density spike at the event horizon if\n                    <jats:inline-formula>\n                      <jats:tex-math>\n                        \n                      <\/jats:tex-math>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mrow>\n                          <mml:mi>\u2113<\/mml:mi>\n                          <mml:mo>&gt;<\/mml:mo>\n                          <mml:mn>0<\/mml:mn>\n                        <\/mml:mrow>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    ; on the contrary, they sometimes exhibit a small dip there. When\n                    <jats:inline-formula>\n                      <jats:tex-math>\n                        \n                      <\/jats:tex-math>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mrow>\n                          <mml:mi>\u2113<\/mml:mi>\n                          <mml:mo>=<\/mml:mo>\n                          <mml:mn>0<\/mml:mn>\n                        <\/mml:mrow>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    , a spike can appear, but its contribution to the total mass density is always negligible. The size, density, and lifetime of these objects vary significantly depending on the parameters, being in some cases as large as galaxies, as dilute as dark matter, and as long-lived as the Universe itself.\n                  <\/jats:p>","DOI":"10.1088\/1361-6382\/ae4160","type":"journal-article","created":{"date-parts":[[2026,2,3]],"date-time":"2026-02-03T22:54:45Z","timestamp":1770159285000},"page":"045010","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Noble gravitational atoms: self-gravitating black hole scalar wigs with angular momentum number"],"prefix":"10.1088","volume":"43","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3367-9868","authenticated-orcid":true,"given":"Miguel","family":"Alcubierre","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9511-6772","authenticated-orcid":true,"given":"Juan","family":"Barranco","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3133-5957","authenticated-orcid":false,"given":"Argelia","family":"Bernal","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8603-5209","authenticated-orcid":true,"given":"Juan","family":"Carlos Degollado","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9322-3083","authenticated-orcid":true,"given":"Alberto","family":"Diez-Tejedor","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0224-9611","authenticated-orcid":true,"given":"Miguel","family":"Megevand","sequence":"additional","affiliation":[]},{"given":"Dar\u00edo","family":"N\u00fa\u00f1ez","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0753-4449","authenticated-orcid":true,"given":"Olivier","family":"Sarbach","sequence":"additional","affiliation":[]}],"member":"266","published-online":{"date-parts":[[2026,2,18]]},"reference":[{"key":"cqgae4160bib1","doi-asserted-by":"publisher","first-page":"214","DOI":"10.1086\/154711","type":"journal-article","article-title":"Star distribution around a massive black hole in a globular cluster","volume":"209","author":"Bahcall","year":"1976","journal-title":"Astrophys. 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