- Email: [email protected]
Erratum to “Superradiant instability for black holes immersed in a magnetic field” [Phys. Lett. B 666 (2008) 283]
Physics Letters B 670 (2009) 459
Contents lists available at ScienceDirect
Physics Letters B www.elsevier.com/locate/physletb
Erratum
Erratum to “Superradiant instability for black holes immersed in a magnetic field” [Phys. Lett. B 666 (2008) 283] R.A. Konoplya Department of Physics, Kyoto University, Kyoto 606-8501, Japan
a r t i c l e
i n f o
a b s t r a c t
Article history: Received 22 November 2008 Accepted 24 November 2008 Available online 28 November 2008 Editor: M. Cvetiˇc
This is the erratum to the Letter [R.A. Konoplya, Phys. Lett. B 666 (2008) 283]. The formulas (18)–(20) are corrected, though the conclusions of the work have not changed. © 2008 Elsevier B.V. All rights reserved.
In [1] Eqs. (18)–(20) should read as follows:
ω=
μ2 + B 2 m 2
γ = μ2 + B 2 m 2 M ×
1−
2
2 2 ( μ + B 2 m2 ) M + iγ , +1+n
μ2 + B 2 m 2
amM −1 − 2
amM −1 − 2
μ2 + B 2m2 r+ > 0,
4+4
j 1 − a2 / M 2 + (am/ M ) − 2
j =1
(1)
μ2 + B 2 m 2 r +
B BM.
μ2 + B 2 m 2 r + 2
,
24+2 (2 + 1 + n)! n!( + 1 + n)2+4
! (2)!(2 + 1)!
2
(2)
(3)
As a result Fig. 3 in [1] is slightly corrected, see Fig. 1. This does not effect neither any other part of the article [1], nor physical conclusions related in [1].
Fig. 1. The growth/damping rate γ as a function of the dimensionless parameter B M for massive scalar field: = m = 1, n = 0, a = 0.1, μ M = 0.1 (left), μ M = 0.05, μ M = 0.01 (right). One can see that there is no superradiant instability for cases μ = 0.1 and 0.05 as for those beyond the inequality (20). The superradiant instability growth rate, plotted in the right figure, is shown to be increased by a few times because of the presence of the magnetic field.
References [1] R.A. Konoplya, Phys. Lett. B 666 (2008) 283.
DOI of original article: 10.1016/j.physletb.2008.07.079. E-mail address: [email protected]. 0370-2693/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.physletb.2008.11.059
Contents lists available at ScienceDirect
Physics Letters B www.elsevier.com/locate/physletb
Erratum
Erratum to “Superradiant instability for black holes immersed in a magnetic field” [Phys. Lett. B 666 (2008) 283] R.A. Konoplya Department of Physics, Kyoto University, Kyoto 606-8501, Japan
a r t i c l e
i n f o
a b s t r a c t
Article history: Received 22 November 2008 Accepted 24 November 2008 Available online 28 November 2008 Editor: M. Cvetiˇc
This is the erratum to the Letter [R.A. Konoplya, Phys. Lett. B 666 (2008) 283]. The formulas (18)–(20) are corrected, though the conclusions of the work have not changed. © 2008 Elsevier B.V. All rights reserved.
In [1] Eqs. (18)–(20) should read as follows:
ω=
μ2 + B 2 m 2
γ = μ2 + B 2 m 2 M ×
1−
2
2 2 ( μ + B 2 m2 ) M + iγ , +1+n
μ2 + B 2 m 2
amM −1 − 2
amM −1 − 2
μ2 + B 2m2 r+ > 0,
4+4
j 1 − a2 / M 2 + (am/ M ) − 2
j =1
(1)
μ2 + B 2 m 2 r +
B BM.
μ2 + B 2 m 2 r + 2
,
24+2 (2 + 1 + n)! n!( + 1 + n)2+4
! (2)!(2 + 1)!
2
(2)
(3)
As a result Fig. 3 in [1] is slightly corrected, see Fig. 1. This does not effect neither any other part of the article [1], nor physical conclusions related in [1].
Fig. 1. The growth/damping rate γ as a function of the dimensionless parameter B M for massive scalar field: = m = 1, n = 0, a = 0.1, μ M = 0.1 (left), μ M = 0.05, μ M = 0.01 (right). One can see that there is no superradiant instability for cases μ = 0.1 and 0.05 as for those beyond the inequality (20). The superradiant instability growth rate, plotted in the right figure, is shown to be increased by a few times because of the presence of the magnetic field.
References [1] R.A. Konoplya, Phys. Lett. B 666 (2008) 283.
DOI of original article: 10.1016/j.physletb.2008.07.079. E-mail address: [email protected]. 0370-2693/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.physletb.2008.11.059