{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/instability-of-the-massive-klein-gordon-field","title":"Instability of the massive Klein-Gordon field on the Kerr spacetime","arxiv_id":"0705.2880","date":"2007-05-20","proceeding":null,"authors":["Sam R. Dolan"],"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.","url_abs":"https://arxiv.org/abs/0705.2880v2","url_pdf":"https://arxiv.org/pdf/0705.2880v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"instability-of-the-massive-klein-gordon-field","repo_url":"https://github.com/vedantdhruv96/superradiance_modes","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}