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The CO core collapse generates a newborn NS and a supernova that triggers the GRB by accreting onto the NSs, rapidly transferring mass and angular momentum to them. This article aims to determine the conditions under which a black hole (BH) forms from NS collapse induced by the accretion and the impact on the GRB\u2019s observational properties and taxonomy. We perform three-dimensional, smoothed particle hydrodynamics simulations of BdHNe using up-to-date NS nuclear equations of state, with and without hyperons, and calculate the structure evolution in full general relativity. We assess the binary parameters leading either NS in the binary to the critical mass for gravitational collapse into a BH and its occurrence time, <jats:italic>t<\/jats:italic>\n                  <jats:sub>col<\/jats:sub>. We include a nonzero angular momentum of the NSs and find that <jats:italic>t<\/jats:italic>\n                  <jats:sub>col<\/jats:sub> ranges from a few tens of seconds to hours for decreasing NS initial angular momentum values. BdHNe I are the most compact (about 5 minute orbital period), promptly form a BH, and release \u227310<jats:sup>52<\/jats:sup> erg of energy. They form NS\u2013BH binaries with tens of kiloyears merger timescales by gravitational-wave emission. BdHNe II and III do not form BHs, and release \u223c10<jats:sup>50<\/jats:sup>\u201310<jats:sup>52<\/jats:sup> erg and \u227210<jats:sup>50<\/jats:sup> erg of energy, respectively. They form NS\u2013NS binaries with a range of merger timescales larger than for NS\u2013BH binaries. In some compact BdHNe II, either NS can become supramassive, i.e., above the critical mass of a nonrotating NS. Magnetic braking by a 10<jats:sup>13<\/jats:sup> G field can delay BH formation, leading to BH\u2013BH or NS\u2013BH with tens of kiloyears merger timescales.<\/jats:p>","DOI":"10.3847\/1538-4357\/ad82ea","type":"journal-article","created":{"date-parts":[[2024,11,14]],"date-time":"2024-11-14T07:38:41Z","timestamp":1731569921000},"page":"80","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":4,"title":["Occurrence of Gravitational Collapse in the Accreting Neutron Stars of Binary-driven Hypernovae"],"prefix":"10.3847","volume":"976","author":[{"given":"L. M.","family":"Becerra","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7894-1028","authenticated-orcid":true,"given":"F.","family":"Cipolletta","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2624-0056","authenticated-orcid":true,"given":"C. 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