Non-Rotating BTZ Black Hole Area Spectrum from Quasi-normal Modes

M. R. Setare

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Non-Rotating BTZ Black Hole Area Spectrum from Quasi-normal Modes

M. R. Setare

High Energy Physics - Theory · Submitted 23 Nov 2003

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In this paper, by using the quasi-normal frequencies for non-rotating BTZ black hole derived by Cardos and Lemos, also via Bohr-Sommerfeld quantization for an adiabatic invariant, $I=\int {dE\over \omega(E)}$, which $E$ is the energy of system and $\omega(E)$ is vibrational frequency, we leads to an equally spaced mass spectrum.

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In this paper, by using the quasi-normal frequencies for non-rotating BTZ black hole derived by Cardos and Lemos, also via Bohr-Sommerfeld quantization for an adiabatic invariant, $I=\int {dE\over \omega(E)}$, which $E$ is the energy of system and $\omega(E)$ is vibrational frequency, we leads to an equally spaced mass spectrum. The result for the area of event horizon is $A_{n}=2\pi \sqrt{\frac{nm \hbar}{\Lambda}}$ which is not equally spaced, in contrast with area spectrum of black hole in higher dimension.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	In this paper, by using the quasi-normal frequencies for non-rotating BTZ black hole derived by Cardos and Lemos, also via Bohr-Sommerfeld quantization for an adiabatic invariant, $I=\int {dE\over \omega(E)}$, which $E$ is the energy of system and $\omega(E)$ is vibrational frequency, we leads to an equally spaced mass spectrum.	method 0.51	0.87	0.64	asserted 1.00
s1	The result for the area of event horizon is $A_{n}=2\pi \sqrt{\frac{nm \hbar}{\Lambda}}$ which is not equally spaced, in contrast with area spectrum of black hole in higher dimension.	result 0.99	0.85	0.35	asserted 1.00

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Original abstract

In this paper, by using the quasi-normal frequencies for non-rotating BTZ black hole derived by Cardos and Lemos, also via Bohr-Sommerfeld quantization for an adiabatic invariant, $I=\int {dE\over \omega(E)}$, which $E$ is the energy of system and $\omega(E)$ is vibrational frequency, we leads to an equally spaced mass spectrum. The result for the area of event horizon is $A_{n}=2\pi \sqrt{\frac{nm \hbar}{\Lambda}}$ which is not equally spaced, in contrast with area spectrum of black hole in higher dimension.

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Using Eq. ([ref]) in ([ref]), when $b_2=0$, we get [equation] The line element ([ref]) is asymptotically approaching AdS/dS spacetime and does not coincide with the BTZ spacetime due to the contribution of the extra terms that come mainly from the constant $c_1$ whose source is the effect of higher-order curvature terms of $𝑓(𝑅)$ [ref] .

New black hole solutions in three-dimensional $\mathit{f(R)}$ gravity · Physical properties of the non-rotating BH solution, Eq. ([ref]) · 0.97

Cites it as background 5 papers

Through the interpretation that identifying the vibrational frequency $Δω(E)$ as the quasinormal modes, much work has been done (e.g., [ref] ), where the vibrational frequency $Δω(E)$ was regarded as the real part of the quasinormal modes.

Area Spectrum of the Large AdS Black Hole from Quasinormal Modes · Area spectrum of the 3-dimensional large AdS black hole · 0.92
Hod's ideas caused significant interest in the problem within the scientific community and considerable amount of work followed Hod's original paper (e.g. see the papers [ref] ).

Quasi-normal modes, area spectra and multi-horizon spacetimes · Introduction · 0.98
This rejuvenates a great interest in the investigation of the black hole area and entropy spectra via the interpretation of the QNM frequencies [ref] .

Black hole spectroscopy from null geodesics · Introduction · 0.81

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