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Quasinormal frequencies of asymptotically anti-de Sitter black holes in two dimensions
General Relativity and Quantum Cosmology · Submitted 17 Jan 2012
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We use their values to discuss the classical stability of the quasinormal modes in uncharged Achucarro-Ortiz black hole and to check the recently proposed Time Times Temperature bound.
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The abstract, sentence by sentence
We calculate exactly the quasinormal frequencies of Klein-Gordon and Dirac test fields propagating in two-dimensional uncharged Achucarro-Ortiz black hole. For both test fields we study whether the quasinormal frequencies are well defined in the massless limit. We use their values to discuss the classical stability of the quasinormal modes in uncharged Achucarro-Ortiz black hole and to check the recently proposed Time Times Temperature bound. Furthermore we extend some of these results to the charged Achucarro-Ortiz black hole.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We calculate exactly the quasinormal frequencies of Klein-Gordon and Dirac test fields propagating in two-dimensional uncharged Achucarro-Ortiz black hole. | contribution 0.87 | 0.97 | 0.29 | asserted 1.00 |
| s1 | For both test fields we study whether the quasinormal frequencies are well defined in the massless limit. | contribution 0.99 | 0.89 | 0.05 | unclear 0.68 |
| s2 | We use their values to discuss the classical stability of the quasinormal modes in uncharged Achucarro-Ortiz black hole and to check the recently proposed Time Times Temperature bound. | contribution 0.56 | 0.92 | 0.24 | asserted 0.89 |
| s3 | Furthermore we extend some of these results to the charged Achucarro-Ortiz black hole. | contribution 0.99 | 0.94 | 0.06 | asserted 0.98 |
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The paper
Original abstract
We calculate exactly the quasinormal frequencies of Klein-Gordon and Dirac test fields propagating in two-dimensional uncharged Achucarro-Ortiz black hole. For both test fields we study whether the quasinormal frequencies are well defined in the massless limit. We use their values to discuss the classical stability of the quasinormal modes in uncharged Achucarro-Ortiz black hole and to check the recently proposed Time Times Temperature bound. Furthermore we extend some of these results to the charged Achucarro-Ortiz black hole.
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How the literature uses it
6 arXiv papers cite this in 33 sentences
Papers citing it · 22 sentences without a confident label
Builds on it 1 paper
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Therefore we extend the results of Ref. [ref] to analyze whether the dependence on the black hole physical parameters is of the same form for the values that are not previously explored and we calculate the spectrum of QNFs for the Dirac field.
Quasinormal frequencies of the dimensionally reduced BTZ black hole · Introduction · 1.00
Uses its method or tool 1 paper
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In Appendix [ref] we expound the necessary steps to transform the differential equations ([ref]) into an appropriate form to use the Horowitz-Hubeny method [ref] , but as in Ref. [ref] , the Horowitz-Hubeny method only works for DRBTZ black holes whose horizons radii satisfy $r_+ > 2 r_-$.
Quasinormal frequencies of the dimensionally reduced BTZ black hole · QNFs of the Dirac field · 0.81
Compares with it 3 papers
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In comparison, we introduce the QNFs for the AdS$_2$ black hole [ref] ω_AO/2πT_H=-i(n+1+√(1+4m^2ℓ^2)/2) which is purely imaginary.
Quasinormal frequencies and thermodynamic quantities for the Lifshitz black holes · 2D Lifshitz black hole · 0.99
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We notice that the QNFs ([ref]) are purely imaginary and we also comment that for the Klein-Gordon field propagating in the DRBTZ black hole, we numerically obtain purely imaginary QNFs (see also Refs. [ref] , [ref] , [ref] ).
Quasinormal frequencies of the dimensionally reduced BTZ black hole · Numerical results · 0.87
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A relevant fact is that its QNFs are complex, in contrast to other asymptotically adS 2D black hole in which purely imaginary QNFs are found [ref] .
Quasinormal frequencies of a two-dimensional asymptotically anti-de Sitter black hole of the dilaton gravity theory · Discussion · 0.96
Cites it as background 2 papers
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As usual for asymptotically adS black holes, we define the QNMs as the oscillations that satisfy the boundary conditions [ref] – [ref] , [ref] , [ref] – [ref] a) The field is purely ingoing near the horizon. b) The field goes to zero as $r →∞$.
Quasinormal frequencies of a two-dimensional asymptotically anti-de Sitter black hole of the dilaton gravity theory · Two-dimensional asymptotically anti-de Sitter black hole · 0.85
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The properties of these 2D black holes are widely studied [ref] , [ref] , [ref] , [ref] , [ref] .
Quasinormal frequencies of the dimensionally reduced BTZ black hole · Introduction · 0.94
What it cites · 69 sentences without a confident label
Contests 2 papers
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Furthermore in the last reference it is shown that in asymptotically flat two-dimensional black holes the massless Klein-Gordon and Dirac fields do not have well defined QNM and hence the frequencies calculated in [ref] cannot be QNF of the massless Dirac field in the uncharged Witten black hole.[See also Refs. [ref] to find the analytical calculation of the asymptotic QNF for the coupled to dilaton Klein-Gordon field in one family of two-dimensional black holes [ref] and the computation with the WKB method of the first QNF for the charged Witten black hole [ref] . ]
Quasinormal modes of stringy black holes · Introduction · contest 0.79
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Furthermore in the last reference it is shown that in asymptotically flat two-dimensional black holes the massless Klein-Gordon and Dirac fields do not have well defined QNM and hence the frequencies calculated in [ref] cannot be QNF of the massless Dirac field in the uncharged Witten black hole.[See also Refs. [ref] to find the analytical calculation of the asymptotic QNF for the coupled to dilaton Klein-Gordon field in one family of two-dimensional black holes [ref] and the computation with the WKB method of the first QNF for the charged Witten black hole [ref] . ]
Quasinormal modes for single horizon black holes in generic 2-d dilaton gravity · Introduction · contest 0.79
Builds on 1 paper
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In a similar way to [ref] , we see that for asymptotically anti-de Sitter two-dimensional black holes the massless Klein-Gordon equation simplifies to a free Schrödinger type equation (see Eqs. (25) and (26) in [ref] ), and since its solutions do not satisfy the boundary conditions of the QNM, we find that the massless Klein-Gordon field does not have well defined QNF in asymptotically anti-de Sitter two-dimensional black holes.
Quasinormal frequencies of asymptotically flat two-dimensional black holes · Quasinormal frequencies of the Klein-Gordon field · 0.80
Uses the method or tool of 6 papers
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To calculate numerically the QNF of the massive Klein-Gordon field in CAO black hole we exploit the method proposed by Horowitz and Hubeny [ref] that allows us to compute numerically the QNF of asymptotically anti-de Sitter black holes (see also [ref] ).
Quasinormal modes of black holes and black branes · Numerical method · 1.00
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To calculate numerically the QNF of the massive Klein-Gordon field in CAO black hole we exploit the method proposed by Horowitz and Hubeny [ref] that allows us to compute numerically the QNF of asymptotically anti-de Sitter black holes (see also [ref] ).
Quasinormal modes of black holes: from astrophysics to string theory · Numerical method · 1.00
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To calculate numerically the QNF of the massive Klein-Gordon field in CAO black hole we exploit the method proposed by Horowitz and Hubeny [ref] that allows us to compute numerically the QNF of asymptotically anti-de Sitter black holes (see also [ref] ).
Scalar, electromagnetic and Weyl perturbations of BTZ black holes: quasi normal modes · Numerical method · 1.00
Compares with 9 papers
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Thus to satisfy the boundary condition at infinity we must solve the equations [equation] From these conditions we get that in UAO black hole the QNF of the massive Klein-Gordon field are equal to [equation] Note that the QNF of the Klein-Gordon field in UAO black hole are purely imaginary as those of Refs. [ref] – [ref] for lower dimensional gravitational systems.
Quasinormal Modes of Charged Dilaton Black Holes in 2+1 Dimensions · Quasinormal frequencies of the Klein-Gordon field · 0.88
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Thus to satisfy the boundary condition at infinity we must solve the equations [equation] From these conditions we get that in UAO black hole the QNF of the massive Klein-Gordon field are equal to [equation] Note that the QNF of the Klein-Gordon field in UAO black hole are purely imaginary as those of Refs. [ref] – [ref] for lower dimensional gravitational systems.
Quasinormal frequencies of asymptotically flat two-dimensional black holes · Quasinormal frequencies of the Klein-Gordon field · 0.88
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In contrast to the black holes studied in Refs. [ref] – [ref] , [ref] the UAO and CAO black holes are asymptotically anti-de Sitter.
Quasinormal modes for single horizon black holes in generic 2-d dilaton gravity · Introduction · 0.96
Cites as support 1 paper
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For these reasons, in what follows we calculate numerically the QNF of the minimally coupled massive Klein-Gordon field, since we expect that the massless Klein-Gordon field does not have well defined QNF (see Subsection [ref] and Ref. [ref] ).
Quasinormal frequencies of asymptotically flat two-dimensional black holes · Quasinormal frequencies of the CAO black hole · 0.97
Cites as background 14 papers
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For two-dimensional black holes we know the exact calculations of the QNF that appear in Refs. [ref] – [ref] .
Non-minimal scalar fields in 2D de Sitter and dilaton black holes · Introduction · 0.80
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For two-dimensional black holes we know the exact calculations of the QNF that appear in Refs. [ref] – [ref] .
Quasinormal frequencies of asymptotically flat two-dimensional black holes · Introduction · 0.80
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For a $D$-dimensional spherically symmetric spacetime of the form [equation] where $f$ is a function of the coordinate $r$ and $Ω^2_D-2$ is the line element of a $(D-2)$-dimensional sphere, it is well known that the equations of motion for perturbation fields simplify to Schrödinger type equations [ref] – [ref] [equation] where $V$ is an effective potential that depends on the type of perturbation and $U$ is related to the radial function.
Quasi-Normal Modes of Stars and Black Holes · Numerical method · 0.84
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