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

Setare, M. R.

doi:10.1007/s10714-005-0125-9

Cited by 35 publications

(22 citation statements)

References 39 publications

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“…Attempts to extend these ideas to other black holes were first performed in [97,98] but, as we have computed in the present work, the asymptotic frequencies used in those papers turned out not to be the correct ones to use.…”

Section: The Quantum Of Area From Quasinormal Frequenciesmentioning

confidence: 84%

On the classification of asymptotic quasinormal frequencies for {$d$}-dimensional black holes and quantum gravity

Natário¹,

Schiappa²

2004

Advances in Theoretical and Mathematical Physics

203

595

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We provide a complete classification of asymptotic quasinormal frequencies for static, spherically symmetric black hole spacetimes in d dimensions. This includes all possible types of gravitational perturbations (tensor, vector and scalar type) as described by the Ishibashi-Kodama master equations. The frequencies for Schwarzschild are dimension independent, while for Reissner-Nordström are dimension dependent (the extremal Reissner-Nordström case must be considered separately from the non-extremal case). For Schwarzschild de Sitter, there is a dimension independent formula for the frequencies, except in dimension d = 5 where the formula is different. For Reissner-Nordström de Sitter there is a dimension dependent formula for the frequencies, except in dimension d = 5 where the formula is different. Schwarzschild and Reissner-Nordström Anti-de Sitter black hole spacetimes are simpler: the formulae for the frequencies will depend upon a parameter related to the tortoise coordinate at spatial infinity, and scalar type perturbations in dimension d = 5 lead to a continuous spectrum for the quasinormal frequencies. We also address non-black hole spacetimes, such as pure de Sitter spacetimewhere there are quasinormal modes only in odd dimensions-and pure Anti-de Sitter spacetime-where again scalar type perturbations in dimension d = 5 lead to a continuous spectrum for the normal frequencies. Our results match previous numerical calculations with great accuracy. Asymptotic quasinormal frequencies have also been applied in the framework of quantum gravity for black holes. Our results show that it is only in the simple Schwarzschild case which is possible to obtain sensible results concerning area quantization or loop quantum gravity. In an effort to keep this paper self-contained we also review earlier results in the literature.

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Section: The Quantum Of Area From Quasinormal Frequenciesmentioning

confidence: 84%

On the classification of asymptotic quasinormal frequencies for {$d$}-dimensional black holes and quantum gravity

Natário¹,

Schiappa²

2004

Advances in Theoretical and Mathematical Physics

203

595

View full text Add to dashboard Cite

show abstract

“…There were many proposals to obtain the area spectrum for various black holes since then. Earlier methods of quantizing the horizon area are mostly based on real or imaginary parts of the quasinormal modes [3][4][5][6][7][8][9][10][11][12]. Recently the application of an adiabatic invariant action variable did not use the quasinormal modes [13,14] and the idea of quantizing the angular momentum to obtain the area spectrum first appeared in the study of non-extremal RN black holes [15].…”

Section: Area Law and Logarithmic Correctionmentioning

confidence: 99%

Nonthermal correction to black hole spectroscopy

Wen

2015

Eur. Phys. J. C

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Area spectrum of black holes has been obtained via various methods such as quasinormal modes, adiabatic invariance and angular momentum. Among those methods, calculations were done by assuming black holes in thermal equilibrium. Nevertheless, black holes in the asymptotically flat space usually have a negative specific heat and therefore tend to stay away from thermal equilibrium. Even for black holes with a positive specific heat, the temperature may still not be well defined in the process of radiation, due to the back reaction of a decreasing mass. With respect to these facts, it is very likely that Hawking radiation is nonthermal and the area spectrum is no longer equidistant. In this note, we would like to illustrate how the area spectrum of black holes is corrected by this nonthermal effect. Area law and logarithmic correctionA finite size system often displays a discrete energy spectrum as regards quantum fluctuations. It was suggested that since the dynamics of a black hole is uniquely determined by its charge(s), which is closely related to the finite region enclosed by the horizon, one expects the mass or area spectrum to display a similar discreteness [1,2]. There were many proposals to obtain the area spectrum for various black holes since then. Earlier methods of quantizing the horizon area are mostly based on real or imaginary parts of the quasinormal modes [3][4][5][6][7][8][9][10][11][12]. Recently the application of an adiabatic invariant action variable did not use the quasinormal modes [13,14] and the idea of quantizing the angular momentum to obtain the area spectrum first appeared in the study of non-extremal RN black holes [15]. The various methods of quantization have settled on a spectrum of equidistant discreteness,a

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“…, where E is the energy of system and ω(E) is the vibrational frequency, has an equally spaced spectrum, i.e., I ≈ nh, applying the Bohr-Sommerfeld 1 Similar works on evaluating the area spectrum of other types of black holes are [39][40][41].…”

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confidence: 99%

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

Cited by 35 publications

References 39 publications

On the classification of asymptotic quasinormal frequencies for {$d$}-dimensional black holes and quantum gravity

On the classification of asymptotic quasinormal frequencies for {$d$}-dimensional black holes and quantum gravity

Nonthermal correction to black hole spectroscopy

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

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