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On the Time Times Temperature Bound
General Relativity and Quantum Cosmology · Submitted 28 Jun 2010
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We find that for some of these spacetimes their fundamental quasinormal frequencies do not satisfy the bound proposed by Hod.
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The abstract, sentence by sentence
Recently Hod proposes a lower bound on the relaxation time of a perturbed thermodynamic system. For gravitational systems this bound transforms into a condition on the fundamental quasinormal frequency. We test the bound in some spacetimes whose quasinormal frequencies are calculated exactly, as the three-dimensional BTZ black hole, the D-dimensional de Sitter spacetime, and the D-dimensional Nariai spacetime. We find that for some of these spacetimes their fundamental quasinormal frequencies do not satisfy the bound proposed by Hod.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Recently Hod proposes a lower bound on the relaxation time of a perturbed thermodynamic system. | background 1.00 | 0.03 | 0.03 | asserted 0.97 |
| s1 | For gravitational systems this bound transforms into a condition on the fundamental quasinormal frequency. | background 0.95 | 0.11 | 0.04 | asserted 1.00 |
| s2 | We test the bound in some spacetimes whose quasinormal frequencies are calculated exactly, as the three-dimensional BTZ black hole, the D-dimensional de Sitter spacetime, and the D-dimensional Nariai spacetime. | method 0.80 | 0.86 | 0.04 | asserted 0.96 |
| s3 | We find that for some of these spacetimes their fundamental quasinormal frequencies do not satisfy the bound proposed by Hod. | result 1.00 | 0.96 | 0.90 | asserted 1.00 |
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The paper
Original abstract
Recently Hod proposes a lower bound on the relaxation time of a perturbed thermodynamic system. For gravitational systems this bound transforms into a condition on the fundamental quasinormal frequency. We test the bound in some spacetimes whose quasinormal frequencies are calculated exactly, as the three-dimensional BTZ black hole, the D-dimensional de Sitter spacetime, and the D-dimensional Nariai spacetime. We find that for some of these spacetimes their fundamental quasinormal frequencies do not satisfy the bound proposed by Hod.
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How the literature uses it
2 arXiv papers cite this in 4 sentences
Papers citing it · 3 sentences without a confident label
Cites it as support 1 paper
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Hence it is reasonable to consider that quasinormal modes could not obtained from the extremal BTZ black hole [ref] .
Nonexistence of quasinormal modes in the extremal BTZ black hole · Discussions · 0.98
What it cites · 83 sentences without a confident label
Contests 1 paper
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Thus the implicit assumption of Ref. [ref] $ℍ = 𝔸$ is not valid.
Quasinormal frequencies of the Dirac field in the massless topological black hole · Introduction · contest 0.89
Uses data or values from 9 papers
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In Ref. [ref] Sachs and Solodukhin find that in the non-rotating BTZ black hole for $μ< -1$ the QNF of the tensor perturbations are[As in Ref. [ref] , in the rest of this section we use units where $l=1$, $r_+=1$.] (see formulas (3.32) and (3.38) of Ref. [ref] ) [equation] whereas $μ> 1$ the QNF are [equation] where [equation]
Quasi-Normal Modes in Topologically Massive Gravity · Three-dimensional BTZ black hole · 0.99
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In the spinning BTZ black hole the QNF of the Klein-Gordon field of mass $μ$ are calculated exactly in Ref. [ref] (see also Ref. [ref] ) [equation] where $m$ is the azimuthal number, and $n=0,1,2,…$, is the mode number.
Choptuik Scaling and Quasinormal Modes in the AdS/CFT Correspondence · Three-dimensional BTZ black hole · 0.95
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In the spinning BTZ black hole the QNF of the Klein-Gordon field of mass $μ$ are calculated exactly in Ref. [ref] (see also Ref. [ref] ) [equation] where $m$ is the azimuthal number, and $n=0,1,2,…$, is the mode number.
Conformal Field Theory Interpretation of Black Hole Quasi-normal Modes · Three-dimensional BTZ black hole · 0.95
Cites as support 1 paper
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This comment and the results of Sect. 3 in Ref. [ref] motivated this work.
Quasinormal frequencies of the Dirac field in the massless topological black hole · $D$-dimensional Nariai spacetime · 0.99
Cites as background 23 papers
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Analyzing how a perturbed thermodynamic system returns to an equilibrium state, and based on information theory and thermodynamics, Hod finds that the relaxation time $τ$ of a perturbed thermodynamic system satisfies [ref] [equation] where $ħ$ denotes the reduced Planck constant, and $T$ stands for the temperature of the system.
Universal Bound on Dynamical Relaxation Times and Black-Hole Quasinormal Ringing · Introduction · 0.82
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In the previous papers the so-called left and right temperatures of the BTZ black hole are defined and used (see also Refs. [ref] , [ref] on the QNM of the spinning BTZ black hole) [equation]
Conformal Field Theory Interpretation of Black Hole Quasi-normal Modes · Three-dimensional BTZ black hole · 0.87
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In the previous papers the so-called left and right temperatures of the BTZ black hole are defined and used (see also Refs. [ref] , [ref] on the QNM of the spinning BTZ black hole) [equation]
Choptuik Scaling and Quasinormal Modes in the AdS/CFT Correspondence · Three-dimensional BTZ black hole · 0.87
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