Linear Mode Stability of the Kerr-Newman Black Hole and Its Quasinormal Modes

Dias, Óscar J. C.; Godazgar, Mahdi; Santos, Jorge E.

doi:10.1103/physrevlett.114.151101

Cited by 82 publications

(130 citation statements)

References 63 publications

(136 reference statements)

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“…[38] for nonextremal Kerr black holes and in Ref. [39] for nonextremal Kerr-Newman black holes. In this work we address whether or not extremal Kerr and RN black holes are mode stable by searching for QNMs with positive imaginary parts.…”

Section: Mode Stability Of Extremal Black Holesmentioning

confidence: 99%

Quasinormal modes of extremal black holes

Richartz

2016

Phys. Rev. D

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The continued fraction method (also known as Leaver's method) is one of the most effective techniques used to determine the quasinormal modes of a black hole. For extremal black holes, however, the method does not work (since, in such a case, the event horizon is an irregular singular point of the associated wave equation). Fortunately, there exists a modified version of the method, devised by Onozawa et al. [Phys. Rev. D 53, 7033 (1996)], which works for neutral massless fields around an extremal Reissner-Nordström black hole. In this paper, we generalize the ideas of Onozawa et al. to charged massless perturbations around an extremal Reissner-Nordström black hole and to neutral massless perturbations around an extremal Kerr black hole. In particular, the existence of damped modes is analysed in detail. Similarities and differences between the results of the original continued fraction method for near extremal black holes and the results of the new continued fraction method for extremal black holes are discussed. Mode stability of extremal black holes is also investigated.

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Section: Mode Stability Of Extremal Black Holesmentioning

confidence: 99%

Quasinormal modes of extremal black holes

Richartz

2016

Phys. Rev. D

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“…We display the dimensionless ratio ω 0 /π T BH for various values of the dimensionless black-hole charge parameter Q/r + , where T BH = (r + − r − )/4π(r 2 + + a 2 ) is the temperature of the corresponding Kerr-Newman black hole. One finds that, for nearextremal Kerr-Newman black holes in the regime Q/r + ≤ 0.9 (this is the regime of black-hole electric charges studied numerically in [36] Kerr-Newman black holes share the same universal relaxation properties in the near-extremal T BH → 0 regime.…”

Section: Introductionmentioning

confidence: 99%

“…This interesting result (to be established below) suggests that neutral Kerr black holes and charged Table 1 Quasinormal resonances of near-extremal charged rotating Kerr-Newman black holes. The data shown refer to the fundamental l = m = 2 gravitational-electromagnetic perturbation mode with ω 0 = 0.01 M −1 [36]. We display the dimensionless ratio ω 0 /π T BH for various values of the dimensionless black-hole charge parameter Q/r + , where T BH = (r + − r − )/4π(r 2 + + a 2 ) is the temperature of the corresponding Kerr-Newman black hole.…”

Section: Introductionmentioning

confidence: 99%

“…In the present paper we shall analyze these numerically computed [36] complex black-hole resonances. In particular, we shall show that the coupled gravitational-electromagnetic perturbations of near-extremal Kerr-Newman black holes are described extremely well by the relation (2) (it is worth emphasizing again that, for charged rotating Kerr-Newman black holes, the simple relaxation spectrum (2) was derived analytically only for the particular case of scalar (s = 0) perturbation modes.…”

Section: Introductionmentioning

confidence: 99%

“…In particular, in a very interesting work, Dias, Godazgar, and Santos [36] have recently provided detailed numerical results for the characteristic quasinormal resonances associated with the coupled gravitational-electromagnetic perturbations of generic KerrNewman black holes.…”

Section: Introductionmentioning

confidence: 99%

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Numerical evidence for universality in the relaxation dynamics of near-extremal Kerr–Newman black holes

Hod

2015

Eur. Phys. J. C

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The coupled gravitational-electromagnetic quasinormal resonances of charged rotating Kerr-Newman black holes are explored. In particular, using the recently published numerical data of Dias et al. (Phys Rev Lett 114:151101, 2015), we show that the characteristic relaxation times τ ≡ 1/ ω 0 of near-extremal Kerr-Newman black holes in the regime Q/r + ≤ 0.9 are described, to a very good degree of accuracy, by the simple universal relation τ × T BH = π −1 (here Q, r + , and T BH are respectively the electric charge, horizon radius, and temperature of the Kerr-Newman black hole, and ω 0 is the fundamental quasinormal resonance of the perturbed black-hole spacetime).

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Massive vector fields in Kerr-Newman and Kerr-Sen black hole spacetimes

Cayuso

Dias

Gray

et al. 2020

J. High Energ. Phys.

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The superradiant instability modes of ultralight massive vector bosons are studied for weakly charged rotating black holes in Einstein-Maxwell gravity (the Kerr-Newman solution) and low-energy heterotic string theory (the Kerr-Sen black hole). We show that in both these cases, the corresponding massive vector (Proca) equations can be fully separated, exploiting the hidden symmetry present in these spacetimes. The resultant ordinary differential equations are solved numerically to find the most unstable modes of the Proca field in the two backgrounds and compared to the vacuum (Kerr black hole) case. black hole with mass M and U (1) charge Q and contains two extra background fields; the scalar dilaton Φ and the 3-form H. In the limit that these two fields vanish the spacetime reduces to the Kerr black hole. On the other hand, this spacetime should be compared to the Kerr-Newman solution [17] which is the unique stationary black hole solution to the Einstein equations with U (1) charge (it can also be understood as a solution of N = 2, D = 4 supergravity). Both Kerr-Newman and Kerr-Sen black holes are stationary and axisymmetric spacetimes, possessing two Killing vectors which aid in understanding the behaviour of test fields in these backgrounds. In the Kerr-Newman case there exists an additional hidden symmetry of the principal Killing-Yano tensor which gives rise to Carter's constant for charged geodesics [18]. For the Kerr-Sen spacetime only a generalized principal tensor with torsion exists which is a weaker but still rather useful structure [19].The aim of this paper is to study the superradiant instabilities of the Kerr-Sen and Kerr-Newman black holes, as triggered by the ultralight massive bosons. These are well understood in the case of massive scalar fields, see [20] and [21], but the corresponding study for massive vectors is currently missing. The reason is simple. Even for vacuum (Kerr) black holes, the corresponding Proca equations are rather complicated partial differential equations whose direct decoupling and separation à la Teukolsky [22,23] does not work due to the presence of the mass term [24,25]. As a consequence the problem was investigated either using approximations [9,24,25] or employing serious numerical analysis [10,26,27].However, a separability renaissance for vector fields has begun in the last couple of years due to a new ansatz by Lunin [28]. Simplified and written in covariant form by Frolov-Krtouš-Kubizňák [29,30], the new ansatz works for the massive vector field case [31] and can be applied in the Kerr-NUT-AdS spacetimes for all dimensions. Importantly the Lunin-Frolov-Krtouš-Kubizňák (LFKK) ansatz exploits the existence of hidden symmetries in these spacetimes which are encoded in the principal tensor [18] and allows the Proca equations to be decoupled and separated into ordinary differential equations [31]. In four dimensions, the separation equally applies to the non-accelerating electro-vacuum type D Plebański-Demiański spacetimes and thence to the Kerr-Newman black holes. 1...

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Linear Mode Stability of the Kerr-Newman Black Hole and Its Quasinormal Modes

Cited by 82 publications

References 63 publications

Quasinormal modes of extremal black holes

Quasinormal modes of extremal black holes

Numerical evidence for universality in the relaxation dynamics of near-extremal Kerr–Newman black holes

Massive vector fields in Kerr-Newman and Kerr-Sen black hole spacetimes

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