Instability of the massive Klein-Gordon field on the Kerr spacetime

被引:381
作者
Dolan, Sam R. [1 ]
机构
[1] Univ Coll Dublin, Sch Math Sci, Dublin 4, Ireland
关键词
D O I
10.1103/PhysRevD.76.084001
中图分类号
P1 [天文学];
学科分类号
0704 ;
摘要
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 less than or similar to 0.5. For a fast rotating hole (a=0.99) we find a maximum growth rate of tau(-1) approximate to 1.5 x 10(-7)(GM/c(3))(-1), at M mu approximate to 0.42. The physical implications are discussed.
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页数:12
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[1]  
Abramowitz M., 1965, HDB MATH FUNCTIONS F, DOI DOI 10.1119/1.15378
[2]   QUASI-NORMAL MODES OF A SCHWARZSCHILD BLACK-HOLE - IMPROVED PHASE-INTEGRAL TREATMENT [J].
ANDERSSON, N ;
LINNAEUS, S .
PHYSICAL REVIEW D, 1992, 46 (10) :4179-4187
[3]   Dynamics of scalar fields in the background of rotating black holes. II. A note on superradiance [J].
Andersson, N ;
Laguna, P ;
Papadopoulos, P .
PHYSICAL REVIEW D, 1998, 58 (08)
[4]   Superradiance resonance cavity outside rapidly rotating black holes [J].
Andersson, N ;
Glampedakis, K .
PHYSICAL REVIEW LETTERS, 2000, 84 (20) :4537-4540
[5]  
[Anonymous], 2006, ASTRON TELEGRAM 6349
[6]  
Baber WG, 1935, P CAMB PHILOS SOC, V31, P564
[7]   Eigenvalues and eigenfunctions of spin-weighted spheroidal harmonics in four and higher dimensions [J].
Berti, E ;
Cardoso, V ;
Casals, M .
PHYSICAL REVIEW D, 2006, 73 (02)
[8]   Stability of five-dimensional rotating black holes projected on the brane [J].
Berti, E ;
Kokkotas, KD ;
Papantonopoulos, E .
PHYSICAL REVIEW D, 2003, 68 (06)
[9]   SOLUTION OF SCALAR WAVE-EQUATION IN A KERR BACKGROUND BY SEPARATION OF VARIABLES [J].
BRILL, DR ;
CHRZANOWSKI, PL ;
FACKERELL, ED ;
IPSER, JR ;
PEREIRA, CM .
PHYSICAL REVIEW D, 1972, 5 (08) :1913-+
[10]  
Burko LM, 2004, PHYS REV D, V70, DOI 10.1103/PhysRevD.70.044018