Area Quantization in Quasi-Extreme Black Holes

Abdalla, Élcio; Castello-Branco, K. H. C.; Lima-Santos, A.

doi:10.1142/s0217732303011435

Cited by 23 publications

(24 citation statements)

References 26 publications

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“…By setting m = 1, the area spectrum (39) is exactly the same with the one derived for the case of quasi-extreme Kerr black hole in [12]. Furthermore, the universal (i.e.…”

Section: Extremal Kerr Black Holesupporting

confidence: 53%

Area Spectrum of Kerr and Extremal Kerr Black Holes From Quasinormal Modes

Setare

Vagenas

2005

Mod. Phys. Lett. A

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Motivated by the recent interest in quantization of black hole area spectrum, we consider the area spectrum of Kerr and extremal Kerr black holes. Based on the proposal by Bekenstein and others that the black hole area spectrum is discrete and equally spaced, we implement Kunstatter's method to derive the area spectrum for the Kerr and extremal Kerr black holes. The real part of the quasinormal frequencies of Kerr black hole used for this computation is of the form mΩ where Ω is the angular velocity of the black hole horizon. The resulting spectrum is discrete but not as expected uniformly spaced. Thus, we infer that the function describing the real part of quasinormal frequencies of Kerr black hole is not the correct one. This conclusion is in agreement with the numerical results for the highly damped quasinormal modes of Kerr black hole recently presented by Berti, Cardoso and Yoshida. On the contrary, extremal Kerr black hole is shown to have a discrete area spectrum which in addition is evenly spaced. The area spacing derived in our analysis for the extremal Kerr black hole area spectrum is not proportional to ln 3. Therefore, it does not give support to Hod's statement that the area spectrum A n = (4l 2 p ln3)n should be valid for a generic Kerr-Newman black hole.

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“…By setting m = 1, the area spectrum (39) is exactly the same with the one derived for the case of quasi-extreme Kerr black hole in [12]. Furthermore, the universal (i.e.…”

Section: Extremal Kerr Black Holesupporting

confidence: 53%

Area Spectrum of Kerr and Extremal Kerr Black Holes From Quasinormal Modes

Setare

Vagenas

2005

Mod. Phys. Lett. A

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“…We will argue that the conclusion of their calculation is in fact wrong, since those authors did not take into account the functional behaviour of ω R (a) (which was unknown when they wrote the paper), but rather assumed that ω R = m/2M is constant in the vicinity of the extremal limit. In following the steps traced out in [22] we will restore for clarity all factors of M . This means, for example, that the asymptotic frequency for m > 0 in the extremal limit is ω R = m/2M .…”

Section: Methodsmentioning

confidence: 99%

“…The hint for an answer necessarily comes from analytical or numerical calculations of highly damped QNM's for charged and rotating black holes, or for black holes in nonasymptotically flat spacetimes. Some calculations in this direction have now been performed, revealing unexpected and puzzling features [12,19,20,21,22,23,24,25,26,27].…”

Section: Introductionmentioning

confidence: 99%

Highly damped quasinormal modes of Kerr black holes

Cardoso²,

et al. 2003

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Motivated by recent suggestions that highly damped black hole quasinormal modes (QNM's) may provide a link between classical general relativity and quantum gravity, we present an extensive computation of highly damped QNM's of Kerr black holes. We perform the computation using two independent numerical codes based on Leaver's continued fraction method. We do not limit our attention to gravitational modes, thus filling some gaps in the existing literature. As already observed in [19], the frequency of gravitational modes with l = m = 2 tends to ωR = 2Ω, Ω being the angular velocity of the black hole horizon. We show that, if Hod's conjecture is valid, this asymptotic behaviour is related to reversible black hole transformations. Other highly damped modes with m > 0 that we computed do not show a similar behaviour. The real part of modes with l = 2 and m < 0 seems to asymptotically approach a constant value ωR ≃ −m̟, ̟ ≃ 0.12 being (almost) independent of a. For any perturbing field, trajectories in the complex plane of QNM's with m = 0 show a spiralling behaviour, similar to the one observed for Reissner-Nordström (RN) black holes. Finally, for any perturbing field, the asymptotic separation in the imaginary part of consecutive modes with m > 0 is given by 2πTH (TH being the black hole temperature). We conjecture that for all values of l and m > 0 there is an infinity of modes tending to the critical frequency for superradiance (ωR = m) in the extremal limit. Finally, we study in some detail modes branching off the so-called "algebraically special frequency" of Schwarzschild black holes. For the first time we find numerically that QNM multiplets emerge from the algebraically special Schwarzschild modes, confirming a recent speculation.

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“…Since its first prediction by Bekenstein in 1974 [1], there has been much work on this topic [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. Recently, the quantization of the black hole area has been considered [5,6], as a result of the absorption of a quasinormal mode excitation.…”

Section: Introductionmentioning

confidence: 99%

Near extremal Schwarzschild-de Sitter black hole area spectrum from quasi-normal modes

Setare

2005

Gen Relativ Gravit

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Using the quasi-normal modes frequency of near extremal Schwarzschild-de Sitter black holes, we obtain area and entropy spectrum for the black hole horizon. By using Bohr-Sommerfeld quantization for an adiabatic invariant, where E is the energy of the system and ω(E) is the vibrational frequency, we arrive at an equally spaced mass spectrum. In the other terms, we extend directly the Kunstatter's approach [7] to determine mass and entropy spectrum of near extremal Schwarzschild-de Sitter black holes which are asymptotically de Sitter rather than asymptotically flat. We show the mass and area spectrum is equally spaced only for a fixed l. For different l there are multiplets with different values of spacing.

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Area Quantization in Quasi-Extreme Black Holes

Abstract: We consider quasi-extreme Kerr and quasi-extreme Schwarzschild-de Sitter black holes. From the known analytical expressions obtained for their quasi-normal modes frequencies, we suggest an area quantization prescription for those objects.Comment: Final version to appear in Mod. Phys. Lett.

Cited by 23 publications

References 26 publications

Area Spectrum of Kerr and Extremal Kerr Black Holes From Quasinormal Modes

Area Spectrum of Kerr and Extremal Kerr Black Holes From Quasinormal Modes

Highly damped quasinormal modes of Kerr black holes

Near extremal Schwarzschild-de Sitter black hole area spectrum from quasi-normal modes

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