The Highly Damped Quasinormal Modes of Extremal Reissner-Nordstr\"om and Reissner-Nordstr\"om-de Sitter Black Holes

Michael Green; Ramin G. Daghigh

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The Highly Damped Quasinormal Modes of Extremal Reissner-Nordstr\"om and Reissner-Nordstr\"om-de Sitter Black Holes

Ramin G. Daghigh, Michael Green

General Relativity and Quantum Cosmology · Submitted 9 Aug 2007

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

The authors' main claim We show that, even though the topology of the Stokes/anti-Stokes lines in the extremal case is different than the non-extremal case, the highly damped quasinormal mode frequencies of extremal black holes match exactly with the extremal limit of the non-extremal black hole quasinormal mode frequencies.

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arXiv ID0708.1333 (version 2)

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CitationMichael Green, Ramin G. Daghigh. "The Highly Damped Quasinormal Modes of Extremal Reissner-Nordstr\"om and Reissner-Nordstr\"om-de Sitter Black Holes." arXiv:0708.1333 (2007). https://pith.science/paper/GUDMB3VV

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We analyze in detail the highly damped quasinormal modes of $D$-dimensional extremal Reissner-Nordstr$\ddot{\rm{o}}$m and Reissner-Nordstr$\ddot{\rm{o}}$m-de Sitter black holes. We only consider the extremal case where the event horizon and the Cauchy inner horizon coincide. We show that, even though the topology of the Stokes/anti-Stokes lines in the extremal case is different than the non-extremal case, the highly damped quasinormal mode frequencies of extremal black holes match exactly with the extremal limit of the non-extremal black hole quasinormal mode frequencies.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We analyze in detail the highly damped quasinormal modes of $D$-dimensional extremal Reissner-Nordstr$\ddot{\rm{o}}$m and Reissner-Nordstr$\ddot{\rm{o}}$m-de Sitter black holes.	contribution 1.00	0.95	0.08	asserted 0.71
s1	We only consider the extremal case where the event horizon and the Cauchy inner horizon coincide.	limitation 0.92	0.72	0.03	asserted 0.91
s2	We show that, even though the topology of the Stokes/anti-Stokes lines in the extremal case is different than the non-extremal case, the highly damped quasinormal mode frequencies of extremal black holes match exactly with the extremal limit of the non-extremal black hole quasinormal mode frequencies.	result 1.00	0.94	0.90	asserted 1.00

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Original abstract

We analyze in detail the highly damped quasinormal modes of $D$-dimensional extremal Reissner-Nordstr$\ddot{\rm{o}}$m and Reissner-Nordstr$\ddot{\rm{o}}$m-de Sitter black holes. We only consider the extremal case where the event horizon and the Cauchy inner horizon coincide. We show that, even though the topology of the Stokes/anti-Stokes lines in the extremal case is different than the non-extremal case, the highly damped quasinormal mode frequencies of extremal black holes match exactly with the extremal limit of the non-extremal black hole quasinormal mode frequencies.

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1 arXiv paper cite this in 12 sentences

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Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 1 paper

Our investigation further supports the idea that the extremal limit of the non-extremal case, where the charge approaches the mass of the black hole in natural units, leads to the same vibrational spectrum as in the extremal case despite the qualitative differences in their topology.

Calculating quasinormal modes of extremal and non-extremal Reissner-Nordstr\"om black holes with the continued fraction method · 0.88

Papers citing it · 7 sentences without a confident label

Contests it 1 paper

Though Hod’s conjecture gained traction for several years, a possible link to a quantum theory of gravity was quickly proven tenuous when the $ln3$ result did not emerge for the 4D Reissner-Nordström BH in Refs. [ref] nor within other multi-horizon BHs inclusive or exclusive of a cosmological constant [ref] .

Asymptotic quasinormal frequencies of different spin fields in $d$-dimensional spherically-symmetric black holes · Introduction · contest 0.78

Compares with it 1 paper

Although $ϑ→μ$ and $n →∞$ are also a set of non-commuting limits (just like $ϑ→0$ and $n →∞$), the extremal limit of the aQNF of the non-extremal Reissner-Nordström BH from Ref. [ref] agrees with the extremal limit of the aQNF for the extremal Reissner-Nordström BH calculated in Ref. [ref] .

Asymptotic quasinormal frequencies of different spin fields in $d$-dimensional spherically-symmetric black holes · Reissner-Nordström and extremal Reissner-Nordström BHs · 0.90

Cites it as background 1 paper

Within the highly-damped regime, the classical oscillations of a perturbed black hole (BH) known as quasinormal frequencies (QNFs) exhibit a linear, unbounded growth in the imaginary component $( 𝕀m {ω} )$ accompanied by a finite value for the real component $( ℝ e { ω} )$ [ref] .

Asymptotic quasinormal frequencies of different spin fields in $d$-dimensional spherically-symmetric black holes · Introduction · 0.95

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