{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,23]],"date-time":"2025-09-23T14:10:45Z","timestamp":1758636645854},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2012,10,20]],"date-time":"2012-10-20T00:00:00Z","timestamp":1350691200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Gen Relativ Gravit"],"published-print":{"date-parts":[[2013,1]]},"DOI":"10.1007\/s10714-012-1470-0","type":"journal-article","created":{"date-parts":[[2012,10,19]],"date-time":"2012-10-19T01:18:37Z","timestamp":1350609517000},"page":"203-227","source":"Crossref","is-referenced-by-count":2,"title":["Stability study of a model for the Klein\u2013Gordon equation in Kerr space-time"],"prefix":"10.1007","volume":"45","author":[{"given":"Horst Reinhard","family":"Beyer","sequence":"first","affiliation":[]},{"given":"Miguel","family":"Alcubierre","sequence":"additional","affiliation":[]},{"given":"Miguel","family":"Megevand","sequence":"additional","affiliation":[]},{"given":"Juan Carlos","family":"Degollado","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2012,10,20]]},"reference":[{"key":"1470_CR1","volume-title":"Pocketbook of Mathematical Functions","year":"1984","unstructured":"Abramowitz, M., Stegun, I.A. (eds.): Pocketbook of Mathematical Functions. Harri Deutsch, Thun (1984)"},{"key":"1470_CR2","unstructured":"Andersson, L., Blue, P.: Hidden symmetries and decay for the wave equation on the Kerr spacetime (2009). [arXiv:0908.2265v2]"},{"key":"1470_CR3","doi-asserted-by":"crossref","first-page":"659","DOI":"10.1007\/s002200100494","volume":"221","author":"HR Beyer","year":"2001","unstructured":"Beyer, H.R.: On the stability of the Kerr metric. Commun. Math. Phys. 221, 659\u2013676 (2001)","journal-title":"Commun. Math. Phys."},{"key":"1470_CR4","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1098\/rspa.2001.0889","volume":"458","author":"HR Beyer","year":"2002","unstructured":"Beyer, H.R.: A framework for perturbations and stability of differentially rotating stars. Proc. R. Soc. Lond. A. 458, 359\u2013380 (2002)","journal-title":"Proc. R. Soc. Lond. A."},{"key":"1470_CR5","unstructured":"Beyer, H.R.: Beyond partial differential equations: A course on linear and quasi-linear abstract hyperbolic evolution equations. In: Springer Lecture Notes in Mathematics 1898. Springer, Berlin (2007)"},{"key":"1470_CR6","doi-asserted-by":"crossref","first-page":"135014","DOI":"10.1088\/0264-9381\/25\/13\/135014","volume":"25","author":"HR Beyer","year":"2008","unstructured":"Beyer, H.R., Craciun, I.: On a new symmetry of the solutions of the wave equation in the background of a Kerr black hole. Class. Quantum Gravit. 25, 135014 (2008)","journal-title":"Class. Quantum Gravit."},{"key":"1470_CR7","doi-asserted-by":"crossref","unstructured":"Beyer, H.R.: On the stability of the massive scalar field in Kerr space-time. J. Math. Phys. 52(1\u201321), 102502 (2011)","DOI":"10.1063\/1.3653840"},{"key":"1470_CR8","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1063\/1.1705193","volume":"8","author":"RH Boyer","year":"1967","unstructured":"Boyer, R.H., Lindquist, R.W.: Maximal analytic extension of the Kerr metric. J. Math. Phys. 8, 265\u2013281 (1967)","journal-title":"J. Math. Phys."},{"key":"1470_CR9","doi-asserted-by":"crossref","first-page":"44039","DOI":"10.1103\/PhysRevD.70.044039","volume":"70","author":"V Cardoso","year":"2004","unstructured":"Cardoso, V., Dias, O.J.C., Lemos, J.P.S., Yoshida, S.: Black-hole bomb and superradiant instabilities. Phys. Rev. D 70, 44039 (2004)","journal-title":"Phys. Rev. D"},{"key":"1470_CR10","doi-asserted-by":"crossref","first-page":"1641","DOI":"10.1103\/PhysRevD.19.1641","volume":"19","author":"JM Cohen","year":"1979","unstructured":"Cohen, J.M., Kegeles, L.S.: Constructive procedure for perturbations of spacetimes. Phys. Rev. D 19, 1641 (1979)","journal-title":"Phys. Rev. D"},{"key":"1470_CR11","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1007\/s00222-010-0309-0","volume":"185","author":"M Dafermos","year":"2011","unstructured":"Dafermos, M., Rodnianski, I.: A proof of the uniform boundedness of solutions to the wave equation on slowly rotating Kerr backgrounds. Invent. Math. 185, 467\u2013559 (2011)","journal-title":"Invent. Math."},{"key":"1470_CR12","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1007\/BF02725534","volume":"15","author":"T Damour","year":"1976","unstructured":"Damour, T., Deruelle, N., Ruffini, R.: On quantum resonances in stationary geometries. Lett. Nuovo Cimento 15, 257 (1976)","journal-title":"Lett. Nuovo Cimento"},{"key":"1470_CR13","doi-asserted-by":"crossref","first-page":"2323","DOI":"10.1103\/PhysRevD.22.2323","volume":"22","author":"SL Detweiler","year":"1980","unstructured":"Detweiler, S.L.: Klein\u2013Gordon equation and rotating black holes. Phys. Rev. D 22, 2323\u20132326 (1980)","journal-title":"Phys. Rev. D"},{"key":"1470_CR14","doi-asserted-by":"crossref","unstructured":"Dolan, S.R.: Instability of the massive Klein\u2013Gordon field on the Kerr spacetime. Phys. Rev. D 76, 084001 (2007)","DOI":"10.1103\/PhysRevD.76.084001"},{"key":"1470_CR15","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1007\/s00220-006-1525-8","volume":"264","author":"F Finster","year":"2006","unstructured":"Finster, F., Kamran, N., Smoller, J., Yau, S.-T.: Decay of solutions of the wave equation in the Kerr geometry. Commun. Math. Phys. 264, 465\u2013503 (2006)","journal-title":"Commun. Math. Phys."},{"key":"1470_CR16","doi-asserted-by":"crossref","first-page":"983","DOI":"10.1143\/PTP.112.983","volume":"112","author":"H Furuhashi","year":"2004","unstructured":"Furuhashi, H., Nambu, Y.: Instability of massive scalar fields in Kerr\u2013Newman spacetime. Prog. Theor. Phys. 112, 983\u2013995 (2004)","journal-title":"Prog. Theor. Phys."},{"key":"1470_CR17","doi-asserted-by":"crossref","first-page":"061502","DOI":"10.1103\/PhysRevD.81.061502","volume":"81","author":"S Hod","year":"2010","unstructured":"Hod, S., Hod, O.: Analytic treatment of the black-hole bomb. Phys. Rev. D 81, 061502 (2010)","journal-title":"Phys. Rev. D"},{"key":"1470_CR18","doi-asserted-by":"crossref","first-page":"320","DOI":"10.1016\/j.physletb.2012.01.054","volume":"708","author":"S Hod","year":"2012","unstructured":"Hod, S.: On the instability regime of the rotating Kerr spacetime to massive scalar perturbations. Phys. Lett. B 708, 320\u2013323 (2012)","journal-title":"Phys. Lett. B"},{"key":"1470_CR19","doi-asserted-by":"crossref","first-page":"24034","DOI":"10.1103\/PhysRevD.71.024034","volume":"71","author":"MJ Strafuss","year":"2005","unstructured":"Strafuss, M.J., Khanna, G.: Massive scalar field instability in Kerr spacetime. Phys. Rev. D 71, 24034 (2005)","journal-title":"Phys. Rev. D"},{"key":"1470_CR20","doi-asserted-by":"crossref","first-page":"4728","DOI":"10.1103\/PhysRevD.54.4728","volume":"54","author":"W Krivan","year":"1996","unstructured":"Krivan, W., Laguna, P., Papadopoulos, P.: Dynamics of scalar fields in the background of rotating black holes. Phys. Rev. D 54, 4728\u20134734 (1996)","journal-title":"Phys. Rev. D"},{"key":"1470_CR21","doi-asserted-by":"crossref","first-page":"3395","DOI":"10.1103\/PhysRevD.56.3395","volume":"56","author":"W Krivan","year":"1997","unstructured":"Krivan, W., Laguna, P., Papadopoulos, P., Andersson, N.: Dynamics of perturbations of rotating black holes. Phys. Rev. D 56, 3395\u20133404 (1997)","journal-title":"Phys. Rev. D"},{"key":"1470_CR22","doi-asserted-by":"crossref","first-page":"124040","DOI":"10.1103\/PhysRevD.73.124040","volume":"73","author":"RA Konoplya","year":"2006","unstructured":"Konoplya, R.A., Zhidenko, A.: Stability and quasinormal modes of the massive scalar field around Kerr black holes. Phys. Rev. D 73, 124040 (2006)","journal-title":"Phys. Rev. D"},{"key":"1470_CR23","volume-title":"Introduction to the Spectral Theory of Operator Pencils","author":"AS Markus","year":"1988","unstructured":"Markus, A.S.: Introduction to the Spectral Theory of Operator Pencils. AMS, Providence (1988)"},{"key":"1470_CR24","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1016\/0003-4916(74)90173-0","volume":"88","author":"V Moncrief","year":"1974","unstructured":"Moncrief, V.: Gravitational perturbations of spherically symmetric systems. I. The exterior problem. Ann. Phys. 88, 323\u2013342 (1974)","journal-title":"Ann. Phys."},{"key":"1470_CR25","doi-asserted-by":"crossref","first-page":"649","DOI":"10.1086\/152445","volume":"185","author":"WH Press","year":"1973","unstructured":"Press, W.H., Teukolsky, S.: Perturbations of a rotating black hole. II. Dynamical stability of the Kerr metric. Astrophys. J. 185, 649\u2013673 (1973)","journal-title":"Astrophys. J."},{"key":"1470_CR26","unstructured":"Reed, M., Simon, B.: Methods of Mathematical Physics, vol. I, II. Academic, New York (1980, 1975)"},{"key":"1470_CR27","doi-asserted-by":"crossref","first-page":"1063","DOI":"10.1103\/PhysRev.108.1063","volume":"108","author":"T Regge","year":"1957","unstructured":"Regge, T., Wheeler, J.A.: Stability of a Schwarzschild singularity. Phys. Rev. 108, 1063\u20131069 (1957)","journal-title":"Phys. Rev."},{"key":"1470_CR28","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-0348-9152-3","volume-title":"An Introduction to Operator Polynomials","author":"L Rodman","year":"1989","unstructured":"Rodman, L.: An Introduction to Operator Polynomials. Birk\u00e4user, Basel (1989)"},{"key":"1470_CR29","doi-asserted-by":"crossref","unstructured":"Rosa, J.G.: The extremal black hole bomb. J High Energy Phys. JHEP06, 015 (2010)","DOI":"10.1007\/JHEP06(2010)015"},{"key":"1470_CR30","doi-asserted-by":"crossref","first-page":"635","DOI":"10.1086\/152444","volume":"185","author":"SA Teukolsky","year":"1973","unstructured":"Teukolsky, S.A.: Perturbations of a rotating black hole. I. Fundamental equations for gravitational, electromagnetic, and neutrino-field perturbations. Astrophys. J. 185, 635\u2013647 (1973)","journal-title":"Astrophys. J."},{"key":"1470_CR31","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-6027-1","volume-title":"Linear Operators in Hilbert Spaces","author":"J Weidmann","year":"1980","unstructured":"Weidmann, J.: Linear Operators in Hilbert Spaces. Springer, New York (1980)"},{"key":"1470_CR32","doi-asserted-by":"crossref","first-page":"1301","DOI":"10.1063\/1.528308","volume":"30","author":"BF Whiting","year":"1989","unstructured":"Whiting, B.F.: Mode stability of the Kerr black hole. J. Math. Phys. 30, 1301\u20131305 (1989)","journal-title":"J. Math. Phys."},{"key":"1470_CR33","doi-asserted-by":"crossref","first-page":"2203","DOI":"10.1063\/1.1665380","volume":"11","author":"FJ Zerilli","year":"1970","unstructured":"Zerilli, F.J.: Tensor harmonics in canonical form for gravitational radiation and other applications. J. Math. Phys. 11, 2203 (1970)","journal-title":"J. Math. Phys."},{"key":"1470_CR34","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1016\/0003-4916(79)90237-9","volume":"118","author":"TJM Zouros","year":"1979","unstructured":"Zouros, T.J.M., Eardley, D.M.: Instabilities of massive scalar perturbations of a rotating black hole. Ann. Phys. 118, 139\u2013155 (1979)","journal-title":"Ann. Phys."}],"container-title":["General Relativity and Gravitation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10714-012-1470-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10714-012-1470-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10714-012-1470-0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,7,4]],"date-time":"2019-07-04T20:41:14Z","timestamp":1562272874000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10714-012-1470-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,10,20]]},"references-count":34,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2013,1]]}},"alternative-id":["1470"],"URL":"https:\/\/doi.org\/10.1007\/s10714-012-1470-0","relation":{},"ISSN":["0001-7701","1572-9532"],"issn-type":[{"value":"0001-7701","type":"print"},{"value":"1572-9532","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,10,20]]}}}