{"paper":{"title":"No-go theorem for spontaneous vectorization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Spontaneous vectorization cannot occur on hairless black holes without ghost or gradient instabilities","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Aofei Sang, Hsu-Wen Chiang, Sebastian Garcia-Saenz","submitted_at":"2026-05-13T13:58:10Z","abstract_excerpt":"Generalized vector-tensor theories of gravity have drawn attention for admitting hairy black hole solutions, thereby circumventing the standard no-hair theorems. It remains an open question, however, how such black holes may form starting from reasonable initial conditions. It has been suggested that vector hair may grow spontaneously as a result of the field developing a negative effective mass squared $-$ the so-called spontaneous vectorization mechanism. We demonstrate that this is not possible if the initial state is a hairless black hole, a result that applies to essentially all stationar"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We demonstrate that this is not possible if the initial state is a hairless black hole, a result that applies to essentially all stationary and axisymmetric solutions of interest in general relativity. More precisely, we prove that the appearance of a negative effective mass squared for the vector field must necessarily be accompanied by ghost- or gradient-type instabilities.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The spacetime is stationary and axisymmetric with an initial hairless black hole background, as stated for solutions of interest in general relativity.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A no-go theorem shows that negative effective mass squared for the vector field in vector-tensor gravity always accompanies ghost or gradient instabilities, blocking spontaneous vectorization in stationary axisymmetric black holes.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Spontaneous vectorization cannot occur on hairless black holes without ghost or gradient instabilities","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"8b3aaab2c22937f8de946fba848ded3f8efba666bc41396fb65675eed61e0c0f"},"source":{"id":"2605.13920","kind":"arxiv","version":1},"verdict":{"id":"00cf334a-25de-4c93-927a-5eb3f8dfb7cc","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T02:58:24.812454Z","strongest_claim":"We demonstrate that this is not possible if the initial state is a hairless black hole, a result that applies to essentially all stationary and axisymmetric solutions of interest in general relativity. More precisely, we prove that the appearance of a negative effective mass squared for the vector field must necessarily be accompanied by ghost- or gradient-type instabilities.","one_line_summary":"A no-go theorem shows that negative effective mass squared for the vector field in vector-tensor gravity always accompanies ghost or gradient instabilities, blocking spontaneous vectorization in stationary axisymmetric black holes.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The spacetime is stationary and axisymmetric with an initial hairless black hole background, as stated for solutions of interest in general relativity.","pith_extraction_headline":"Spontaneous vectorization cannot occur on hairless black holes without ghost or gradient instabilities"},"references":{"count":74,"sample":[{"doi":"","year":1972,"title":"J. D. Bekenstein, Nonexistence of baryon number for static black holes, Phys. Rev. D5, 1239 (1972)","work_id":"dbaf668b-d6fd-4304-8134-65aefdb887fd","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1972,"title":"J. D. Bekenstein, Nonexistence of baryon number for black holes. ii, Phys. Rev. D5, 2403 (1972)","work_id":"b76f3c16-963e-4065-b1aa-5d356e57ad15","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1995,"title":"J. D. Bekenstein, Novel ‘‘no-scalar-hair’’ theorem for black holes, Phys. Rev. D51, R6608 (1995)","work_id":"923ac237-8838-479d-8a6f-2d07ea4972fe","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2012,"title":"Black holes in scalar-tensor gravity","work_id":"325ca14d-1d96-4ffa-87a9-c4cfb4824b54","ref_index":4,"cited_arxiv_id":"1109.6324","is_internal_anchor":true},{"doi":"","year":2014,"title":"Black hole hair in generalized scalar-tensor gravity","work_id":"b027b635-17e2-48be-8996-2b008045e521","ref_index":5,"cited_arxiv_id":"1312.3622","is_internal_anchor":true}],"resolved_work":74,"snapshot_sha256":"e4f5c16b77292e77bf8786c57549418752690357463dd8412493ed8540bd1ba1","internal_anchors":35},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}