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

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.

04.70.-s
field theory: scalar
black hole: rotation
space-time: Kerr
bound state: spectrum
tensor: energy-momentum
Klein-Gordon equation: massive
bound state: decay
stability
superradiance

References(50)

Figures(0)

A Superradiance resonance cavity outside rapidly rotating black holes

Nils Andersson
(
- Southampton U.
)
,
Kostas Glampedakis
(
- Cardiff U.
)

- Phys.Rev.Lett. 84 (2000) 4537-4540
•
e-Print:
- gr-qc/9909050
•
DOI:
- 10.1103/PhysRevLett.84.4537

Dynamics of scalar fields in the background of rotating black holes. 2. A Note on superradiance

Nils Andersson
(
- Tubingen U. and
- Southampton U.
)
,
Pablo Laguna
(
- Penn State U.
)
,
Philippos Papadopoulos
(
- Potsdam, Max Planck Inst.
)

- Phys.Rev.D 58 (1998) 087503
•
e-Print:
- gr-qc/9802059
•
DOI:
- 10.1103/PhysRevD.58.087503

Quasinormal modes of a Schwarzschild black hole: Improved phase-integral treatment

- Phys.Rev.D 46 (1992) 10, 4179
•
DOI:
- 10.1103/PhysRevD.46.4179

- Proc.Cambridge Phil.Soc. 25 564

Eigenvalues and eigenfunctions of spin-weighted spheroidal harmonics in four and higher dimensions

- Phys.Rev.D 73 (2006) 024013,
- Phys.Rev.D 73 (2006) 109902 (erratum)
•
e-Print:
- gr-qc/0511111
•
DOI:
- 10.1103/PhysRevD.73.109902

Gravitational stability of five-dimensional rotating black holes projected on the brane

- Phys.Rev.D 68 (2003) 064020
•
e-Print:
- gr-qc/0306106
•
DOI:
- 10.1103/PhysRevD.68.064020

Solution of the scalar wave equation in a kerr background by separation of variables

D.R. Brill
(
- Maryland U.
)
,
P.L. Chrzanowski
(
- Maryland U.
)
,
C. Martin Pereira
(
- Maryland U.
)
,
E.D. Fackerell
(
- Victoria U.
)
,
J.R. Ipser
(
- Chicago U., EFI and
- Illinois U., Chicago
)

- Phys.Rev.D 5 (1972) 1913-1915
•
DOI:
- 10.1103/PhysRevD.5.1913

Universality of massive scalar field late time tails in black hole space-times

- Phys.Rev.D 70 (2004) 044018
•
e-Print:
- gr-qc/0403018
•
DOI:
- 10.1103/PhysRevD.70.044018

Small Kerr-anti-de Sitter black holes are unstable

Vitor Cardoso
(
- Coimbra U.
)
,
Oscar J.C. Dias
(
- Lisbon, CENTRA and
- Algarve U.
)

- Phys.Rev.D 70 (2004) 084011
•
e-Print:
- hep-th/0405006
•
DOI:
- 10.1103/PhysRevD.70.084011

Superradiant instabilities of rotating black branes and strings

Vitor Cardoso
(
- McDonnell Ctr. Space Sci. and
- Coimbra U.
)
,
Shijun Yoshida
(
- Waseda U., RISE
)

- JHEP 07 (2005) 009
•
e-Print:
- hep-th/0502206
•
DOI:
- 10.1088/1126-6708/2005/07/009

New instability for rotating black branes and strings

Vitor Cardoso
(
- Coimbra U.
)
,
Jose P.S. Lemos
(
- Lisbon, CENTRA and
- Lisbon, IST
)

- Phys.Lett.B 621 (2005) 219-223
•
e-Print:
- hep-th/0412078
•
DOI:
- 10.1016/j.physletb.2005.06.025

Black strings and p-branes are unstable

R. Gregory
(
- Chicago U., EFI
)
,
R. Laflamme
(
- Los Alamos
)

- Phys.Rev.Lett. 70 (1993) 2837-2840
•
e-Print:
- hep-th/9301052
•
DOI:
- 10.1103/PhysRevLett.70.2837

Particle and light motion in a space-time of a five-dimensional rotating black hole

Valeri P. Frolov
(
- Alberta U.
)
,
Dejan Stojkovic
(
- Alberta U.
)

- Phys.Rev.D 68 (2003) 064011
•
e-Print:
- gr-qc/0301016
•
DOI:
- 10.1103/PhysRevD.68.064011

The Black hole bomb and superradiant instabilities

Vitor Cardoso
(
- Coimbra U.
)
,
Oscar J.C. Dias
(
- Algarve U., CENTRA
)
,
Jose P.S. Lemos
(
- Lisbon, CENTRA and
- Lisbon, IST
)
,
Shijun Yoshida
(
- Lisbon, CENTRA and
- Lisbon, IST
)

- Phys.Rev.D 70 (2004) 044039,
- Phys.Rev.D 70 (2004) 049903 (erratum)
•
e-Print:
- hep-th/0404096
•
DOI:
- 10.1103/PhysRevD.70.049903

On Quantum Resonances in Stationary Geometries

T. Damour
(
- Princeton U.
)
,
N. Deruelle
(
- Cambridge U.
)
,
R. Ruffini
(
- Princeton, Inst. Advanced Study and
- Western Australia U.
)

- Lett.Nuovo Cim. 15 (1976) 257-262
•
DOI:
- 10.1007/BF02725534

KLEIN-GORDON EQUATION AND ROTATING BLACK HOLES

Steven L. Detweiler
(
- Yale U.
)

- Phys.Rev.D 22 (1980) 2323-2326
•
DOI:
- 10.1103/PhysRevD.22.2323

- Phys.Lett. PH 437

- Phys.Rev.D 22 10

Exact solutions of Regge-Wheeler equation and quasi-normal modes of compact objects

P.P. Fiziev
(
- Sofiya U.
)

- Class.Quant.Grav. 23 (2006) 2447-2468
•
e-Print:
- gr-qc/0509123
•
DOI:
- 10.1088/0264-9381/23/7/015

Instability of massive scalar fields in Kerr-Newman space-time

Hironobu Furuhashi
(
- Nagoya U.
)
,
Yasusada Nambu
(
- Nagoya U.
)

- Prog.Theor.Phys. 112 (2004) 983-995
•
e-Print:
- gr-qc/0402037
•
DOI:
- 10.1143/PTP.112.983

The fine and hyperfine structure of fermionic levels in gravitational fields

- Rom.J.Phys. 38 (1993) 729-730

On quasilevels in the gravitational field of a black hole

- Class.Quant.Grav. 9 (1992) 667-676
•
DOI:
- 10.1088/0264-9381/9/3/009

Occupation of bound states by electrons in the Schwarzschild field

V. Gal'tsov D
(
- Moscow State U.
)
,
G.V. Pomerantseva
(
- Moscow State U.
)
,
G.A. Chizhov
(
- Moscow State U.
)

- Sov.Phys.J. 26 (1983) 743-745,
- Izv.Vuz.Fiz. 26N8 (1983) 75-77
•
DOI:
- 10.1007/BF00898887

- Sov.Phys.JETP 26 743

The Evolution of circular, nonequatorial orbits of Kerr black holes due to gravitational wave emission

Scott A. Hughes
(
- Caltech and
- Illinois U., Urbana
)

- Phys.Rev.D 61 (2000) 8, 084004,
- Phys.Rev.D 63 (2001) 4, 049902 (erratum),
- Phys.Rev.D 65 (2002) 6, 069902 (erratum),
- Phys.Rev.D 67 (2003) 8, 089901 (erratum),
- Phys.Rev.D 78 (2008) 10, 109902 (erratum),
- Phys.Rev.D 90 (2014) 10, 109904 (erratum)
•
e-Print:
- gr-qc/9910091
•
DOI:
- 10.1103/PhysRevD.65.069902

1-25 of 50
1
2
25 / page