Quasinormal modes of Schwarzschild–anti-de Sitter black holes: Electromagnetic and gravitational perturbations

Cardoso, Vítor; Lemos, José P. S.

doi:10.1103/physrevd.64.084017

Cited by 332 publications

(401 citation statements)

References 33 publications

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“…And connection between QNMs and the decay of perturbations in the dual CFT was first suggested in the work of [16] based on the numerical computation of QNMs for AdSSchwarzschild black holes in several dimensions. QNMs of AdS black holes and BTZ black holes are investigated in [17,18,19,20,21,22,23,24,25,26,27] and those of near extremal black branes are found in [28]. Furthermore in [29], it was shown that the frequencies of QNMs for BTZ black holes are in exact agreement with the location of the poles of the retarded correlation function describing the linear response on the CFT side.…”

Section: Introductionsupporting

confidence: 54%

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Quasinormal modes of D3-brane black holes

Kurita

Sakagami

2003

Phys. Rev. D

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We investigate a method to evaluate quasi-normal modes of D3-brane black holes by wave interpretation of fields on D3-brane based on the Feynman's space-time approach. We perturbatively solve the wave equation which describes propagation of a dilaton wave in a bulk space and its interaction with the D3-brane. The obtained condition for the quasi-normal modes are qualitatively equivalent to that evaluated in the usual scattering of the dilaton in the black 3-brane spacetime in the corresponding supergravity description.

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Section: Introductionsupporting

confidence: 54%

“…In the usual evaluation to QNMs [19,20,21,22,23,24,25,27], their frequencies are characterized by the curvature scale of the black hole space time, i.e. |ωR| ∼ 1.…”

Section: (Q)mentioning

confidence: 99%

Quasinormal modes of D3-brane black holes

Kurita

Sakagami

2003

Phys. Rev. D

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“…For example, if the black hole is small, we expect to find in the gravitational radiation spectra a strong peak located at ω 2 = 4n 2 + l(l + 1) , n = 1, 2, ... [5]. Moreover, some major results in perturbation theory and numerical relativity [27,28], studying the collision of two black holes, with masses of the same order of magnitude, allow us to infer that evolving the collision of two black holes in AdS spacetime, should not bring major differences in relation to our results (though it is of course a much more difficult task, even in perturbation theory).…”

Section: Discussionmentioning

confidence: 99%

Black hole collision with a scalar particle in four-, five-, and seven-dimensional anti–de Sitter spacetimes: Ringing and radiation

Cardoso¹,

Lemos²

2002

Phys. Rev. D

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In this work we compute the spectra, waveforms and total scalar energy radiated during the radial infall of a small test particle coupled to a scalar field into a d-dimensional Schwarzschild-anti-de Sitter black hole. We focus on d = 4, 5 and 7, extending the analysis we have done for d = 3. For small black holes, the spectra peaks strongly at a frequency ω ∼ d−1, which is the lowest pure antide Sitter (AdS) mode. The waveform vanishes exponentially as t → ∞, and this exponential decay is governed entirely by the lowest quasinormal frequency. This collision process is interesting from the point of view of the dynamics itself in relation to the possibility of manufacturing black holes at LHC within the brane world scenario, and from the point of view of the AdS/CFT conjecture, since the scalar field can represent the string theory dilaton, and 4, 5, 7 are dimensions of interest for the AdS/CFT correspondence.

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“…[26], and references therein). Furthermore, the antide Sitter/conformal field theory (AdS/CFT) conjecture [27] has led to an intensive study of black-hole QNM in asymptotically AdS spacetimes in the last few years [28][29][30][31][32][33][34][35][36][37][38][39]. According to the AdS/CFT correspondence, a large static black hole in AdS corresponds to an approximately thermal state in CFT.…”

mentioning

confidence: 99%

Universal bound on dynamical relaxation times and black-hole quasinormal ringing

2007

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From information theory and thermodynamic considerations a universal bound on the relaxation time τ of a perturbed system is inferred, τ ≥h/πT , where T is the system's temperature. We prove that black holes comply with the bound; in fact they actually saturate it. Thus, when judged by their relaxation properties, black holes are the most extreme objects in nature, having the maximum relaxation rate which is allowed by quantum theory.A fundamental problem in thermodynamic and statistical physics is to study the response of a system in thermal equilibrium to an outside perturbation [1][2][3]. In particular, one is typically interested in calculating the relaxation timescale at which the perturbed system returns to a stationary, equilibrium configuration. Can this relaxation time be made arbitrarily small? That the answer may be negative is suggested by the third-law of thermodynamics, according to which the relaxation time of a perturbed system is expected to go to infinity in the limit of absolute zero of temperature. Finite temperature systems are expected to have faster dynamics and shorter relaxation times-how small can these be made? In this Letter we use general results from quantum information theory in order to derive a fundamental bound on the maximal rate at which a perturbed system approaches thermal equilibrium.On another front, deep connections between the world of black-hole physics and the realms of thermodynamics and information theory were revealed by Hawking's theoretical discovery of black-hole radiation [4], and its corresponding temperature and black-hole entropy [5]. These discoveries imply that black holes behave as thermodynamic systems in many respects. Furthermore, black holes have been proven to be very useful in deriving fundamental, static bounds on information storage [6][7][8][9][10][11]. Can one use black holes to obtain deep insights into natural limitations on dynamical relaxation times? Indeed one can, as we shall show below.Quantum information theory and Thermodynamics.-A fundamental question in quantum information theory is what is the maximum rate,İ max , at which information may be transmitted by a signal of duration τ and energy ∆E. The answer to this question was already found in the 1960's (see e.g. [12,13]):(We use units in which k B = G = c = 1.) An outside perturbation to a thermodynamic system is characterized by energy and entropy changes in the system, ∆E and ∆S, respectively. By the complementary relation between entropy and information (entropy as a measure of one's uncertainty or lack of information about the actual internal state of the system [14][15][16]12]), the relation Eq. (1) sets an upper bound on the rate of entropy change [17],where τ is the characteristic timescale for this dynamical process (the relaxation time required for the perturbed system to return to a quiescent state). Taking cognizance of the second-law of thermodynamics, one obtains from Eq. (2)where T is the system's temperature. Thus, according to quantum theory, a thermodynamic system has...

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Quasinormal modes of Schwarzschild–anti-de Sitter black holes: Electromagnetic and gravitational perturbations

Cited by 332 publications

References 33 publications

Quasinormal modes of D3-brane black holes

Quasinormal modes of D3-brane black holes

Black hole collision with a scalar particle in four-, five-, and seven-dimensional anti–de Sitter spacetimes: Ringing and radiation

Universal bound on dynamical relaxation times and black-hole quasinormal ringing

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