Quasinormal modes of black holes and Borel summation

Hatsuda, Yasuyuki

doi:10.1103/physrevd.101.024008

Cited by 96 publications

(61 citation statements)

References 42 publications

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“…The lowest orders have been found to give very accurate results for high-modes. In [33][34][35] the WKB approximation was studied up to 6th order in (7), where it was found that the frequencies ω must satisfy a specific constraint in terms of V and the coefficients V (k) : (8) where N = n + 1/2 with n = 0, 1, 2, . .…”

Section: Qnm With the Wkb Methodsmentioning

confidence: 99%

Anomalous decay rate of quasinormal modes

2020

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The decay timescales of the quasinormal modes of a massive scalar field have an intriguing behaviour: they either grow or decay with increasing angular harmonic numbers , depending on whether the mass of the scalar field is small or large. We identify the properties of the effective potential of the scalar field that leads to this behaviour and characterize it in detail. If the scalar field is non-minimally coupled, considered here, the scalar quasinormal modes will leak into the gravitational wave signal and will have decaying times that are comparable or smaller than those typical in General Relativity. Hence, these modes could be detectable in the future. Finally, we find that the anomalous behaviour in the decay timescales of quasinormal modes is present in a much larger class of models beyond a simple massive scalar field. * mlagos@kicp.uchicago.edu † pedro.ferreira@physics.ox.ac.uk ‡ oliver.tattersall@physics.ox.ac.uk 1 From the publicly available data in [16], one can check that, for any given azimuthal number m, the QNM are such that |ω I | grows with for all values of the BH's dimensionless spin a = J/M 2 .

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Section: Qnm With the Wkb Methodsmentioning

confidence: 99%

Anomalous decay rate of quasinormal modes

2020

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“…We conclude this section with a few observations on the approach proposed in Ref. [25]. First it should be observed that although the Padé transforms,P N N of the series k a k x k /k!…”

Section: The Methodsmentioning

confidence: 85%

“…In this section we shall construct the quasinormal modes of the perturbed Schwarzschild black hole. Although the Padé summation is our method of choice, whenever in doubt, we will also use the Borel-Padé summation [25]. Moreover, all the cases presented in this section have been calculated using the continued fraction method.…”

Section: A the Schwarzschild Black Holementioning

confidence: 99%

Quasinormal modes of black holes. II. Padé summation of the higher-order WKB terms

Matyjasek

Telecka

2019

Phys. Rev. D

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In previous work [1] we proposed an improvement of the WKB-based semianalytic technique of Iyer and Will for calculation of the quasiormal modes of black holes by constructing the Padé approximants of the formal series for ω 2 . It has been demonstrated that (within the domain of applicability) the diagonal Padé transforms P 6 6 and P 6 7 are always in a very good agreement with the numerical results. In this paper we present a further extension of the method. We show that it is possible to reproduce many known numerical results with a great accuracy (or even exactly) if the Padé transforms are constructed from the perturbative series of a really high order. In our calculations the order depends on the problem but it never exceeds 700. For example, the frequencies of the gravitational mode l = 2, n = 0 calculated with the aid of the Padé approximants and within the framework of the continued fractions method agree to 24 decimal places. The use of such a large number of terms is necessary as the stabilization of the quasinormal frequencies can be slow. Our results reveal some unexpected features of the WKB-based approximations and may shed some fresh light on the problem of overtones.

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“…We utilize the efficient and stable methods [24][25][26][27] that have brought a lot of attention recently. One method we adopt is based on the Borel-Padé summation [24]. The other method we use is the so-called higher order WKB-Padé approach suggested first in ref.…”

Section: Resultsmentioning

confidence: 99%

“…In ref. [24], the results obtained by the Borel-Padé summation and Leaver's method [29] were compared and the consistency of the two methods was determined. Here we can see, e.g from Table 1, that the values obtained by the Borel-Padé summation agrees well with that by the WKB-Padé method when the refractive index is not less than 5 and l is greater than n. For example, we take two sets of data, (η = 5, l = 3, n = 3) and (η = 15, l = 3, n = 0), respectively, and find that the two real parts, 1.179851 and 1.203996 in the first set, differ by 2.01%, and 1.319595 and 1.319663 in the second set, just by 0.07%.…”

Section: Quasinormal Mode Frequencymentioning

confidence: 99%

Quasinormal mode and stability of optical black holes in moving dielectrics

Guo

Miao

2020

Phys. Rev. D

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We study the quasinormal mode and stability of optical black holes in moving dielectrics. The results show that the real part of complex frequencies is inversely proportional to but the absolute value of an imaginary part is proportional to a refractive index. We obtain the conditions for forming a black hole horizon in moving dielectrics. Moreover, we investigate the evolution behavior of optical black holes with respect to a refractive index at a high overtone number and find that an optical black hole undergoes one phase transition from an unstable mode to a stable one when the refractive index is big enough.

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Quasinormal modes of black holes and Borel summation

Cited by 96 publications

References 42 publications

Anomalous decay rate of quasinormal modes

Anomalous decay rate of quasinormal modes

Quasinormal modes of black holes. II. Padé summation of the higher-order WKB terms

Quasinormal mode and stability of optical black holes in moving dielectrics

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