{"work":{"id":"707cf298-8ef8-4b34-b984-caf85f6faf76","openalex_id":null,"doi":null,"arxiv_id":"0705.2880","raw_key":null,"title":"Instability of the massive Klein-Gordon field on the Kerr spacetime","authors":null,"authors_text":"S","year":2007,"venue":"gr-qc","abstract":"We investigate the instability of the massive scalar field in the vicinity of a rotating black hole. The instability arises from amplification caused by the classical superradiance effect. The instability affects bound states: solutions to the massive Klein-Gordon equation which tend to zero at infinity. We calculate the spectrum of bound state frequencies on the Kerr background using a continued fraction method, adapted from studies of quasinormal modes. We demonstrate that the instability is most significant for the $l = 1$, $m = 1$ state, for $M \\mu \\lesssim 0.5$. For a fast rotating hole ($a = 0.99$) we find a maximum growth rate of $\\tau^{-1} \\approx 1.5 \\times 10^{-7} (GM/c^3)^{-1}$, at $M \\mu \\approx 0.42$. The physical implications are discussed.","external_url":"https://arxiv.org/abs/0705.2880","cited_by_count":null,"metadata_source":"pith","metadata_fetched_at":"2026-07-10T10:37:01.820607+00:00","pith_arxiv_id":"0705.2880","created_at":"2026-05-10T14:40:32.372274+00:00","updated_at":"2026-07-10T10:37:01.820607+00:00","title_quality_ok":true,"display_title":"Instability of the massive Klein-Gordon field on the Kerr spacetime","render_title":"Instability of the massive Klein-Gordon field on the Kerr spacetime"},"hub":{"state":{"work_id":"707cf298-8ef8-4b34-b984-caf85f6faf76","tier":"hub","tier_reason":"10+ Pith inbound or 1,000+ external citations","pith_inbound_count":19,"external_cited_by_count":null,"distinct_field_count":5,"first_pith_cited_at":"2009-05-28T19:38:46+00:00","last_pith_cited_at":"2026-07-09T09:04:16+00:00","author_build_status":"not_needed","summary_status":"needed","contexts_status":"needed","graph_status":"needed","ask_index_status":"not_needed","reader_status":"not_needed","recognition_status":"not_needed","updated_at":"2026-08-22T05:59:48.179145+00:00","tier_text":"hub"},"tier":"hub","role_counts":[{"context_role":"background","n":7},{"context_role":"method","n":2}],"polarity_counts":[{"context_polarity":"background","n":7},{"context_polarity":"use_method","n":2}],"runs":{},"summary":{},"graph":{},"authors":[]}}