Stability of Squashed Kaluza-Klein Black Holes

Hideki Ishihara; Jiro Soda; Keiju Murata; Masashi Kimura

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Stability of Squashed Kaluza-Klein Black Holes

Masashi Kimura, Keiju Murata, Hideki Ishihara, Jiro Soda

High Energy Physics - Theory · Submitted 27 Dec 2007

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

The authors' main claim The analysis based on the master equations gives a strong evidence for the stability of squashed Kaluza-Klein black holes.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.21 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.06 · mentions code or data availability 0.01.

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The stability of squashed Kaluza-Klein black holes is studied. The squashed Kaluza-Klein black hole looks like five dimensional black hole in the vicinity of horizon and four dimensional Minkowski spacetime with a circle at infinity. In this sense, squashed Kaluza-Klein black holes can be regarded as black holes in the Kaluza-Klein spacetimes. Using the symmetry of squashed Kaluza-Klein black holes, $SU(2)\times U(1)\simeq U(2)$, we obtain master equations for a part of the metric perturbations relevant to the stability. The analysis based on the master equations gives a strong evidence for the stability of squashed Kaluza-Klein black holes. Hence, the squashed Kaluza-Klein black holes deserve to be taken seriously as realistic black holes in the Kaluza-Klein spacetime.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The stability of squashed Kaluza-Klein black holes is studied.	contribution 0.86	0.80	0.04	asserted 0.69
s1	The squashed Kaluza-Klein black hole looks like five dimensional black hole in the vicinity of horizon and four dimensional Minkowski spacetime with a circle at infinity.	background 0.96	0.23	0.03	asserted 0.99
s2	In this sense, squashed Kaluza-Klein black holes can be regarded as black holes in the Kaluza-Klein spacetimes.	background 0.55	0.23	0.05	asserted 0.57
s3	Using the symmetry of squashed Kaluza-Klein black holes, $SU(2)\times U(1)\simeq U(2)$, we obtain master equations for a part of the metric perturbations relevant to the stability.	method 0.98	0.94	0.04	asserted 1.00
s4	The analysis based on the master equations gives a strong evidence for the stability of squashed Kaluza-Klein black holes.	result 0.98	0.93	0.80	hedged possibility 0.60
s5	Hence, the squashed Kaluza-Klein black holes deserve to be taken seriously as realistic black holes in the Kaluza-Klein spacetime.	interpretation 1.00	0.31	0.64	hedged possibility 0.57

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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arXiv listing abstract v3

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The paper

Original abstract

The stability of squashed Kaluza-Klein black holes is studied. The squashed Kaluza-Klein black hole looks like five dimensional black hole in the vicinity of horizon and four dimensional Minkowski spacetime with a circle at infinity. In this sense, squashed Kaluza-Klein black holes can be regarded as black holes in the Kaluza-Klein spacetimes. Using the symmetry of squashed Kaluza-Klein black holes, $SU(2)\times U(1)\simeq U(2)$, we obtain master equations for a part of the metric perturbations relevant to the stability. The analysis based on the master equations gives a strong evidence for the stability of squashed Kaluza-Klein black holes. Hence, the squashed Kaluza-Klein black holes deserve to be taken seriously as realistic black holes in the Kaluza-Klein spacetime.

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References

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Hydrodynamics of simply spinning black holes & hydrodynamics for spinning quantum fluids
hep-th 2020-07 conditional novelty 6.0 of 10

Large simply spinning five-dimensional Anti-de Sitter black holes exhibit hydrodynamic quasinormal modes whose transport coefficients split into longitudinal and transverse families with explicit angular-momentum dependence.
Catastrophic Instability of Small Lovelock Black Holes
gr-qc 2010-08 conditional novelty 6.0 of 10

Small Lovelock black holes are unstable in all dimensions, with tensor modes driving instability in even dimensions and scalar modes in odd dimensions.
Master Equations for Gravitational Perturbations of Static Lovelock Black Holes in Higher Dimensions
gr-qc 2010-08 accept novelty 6.0 of 10

The authors derive master equations for vector and scalar gravitational perturbations of static Lovelock black holes in any dimension, completing the full set alongside their earlier tensor result.
Black Holes in Higher Dimensions
hep-th 2008-01 accept novelty 2.0 of 10

Higher-dimensional vacuum gravity admits rotating black holes with non-spherical horizons (black rings) and multi-component horizons, so four-dimensional black-hole uniqueness does not extend beyond d = 4.

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24 arXiv papers cite this in 35 sentences

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Papers whose main result relates to this one's

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

Another important feature is that the squashed KK black holes are apparently stable and, thereby, let us avoid the Gregory-Laflamme instability.

Evolution of perturbations of squashed Kaluza-Klein black holes: escape from instability · 0.81

Papers citing it · 18 sentences without a confident label

Contests it 1 paper

Fig. [ref] shows that $Tr(S)$ is bounded, and this implies that the spacetime is stable.[ In Fig. 1 in the erratum for [ref] , the curves for $ρ_0/ρ_+ = 30, 50, 100$ apparently looks regular, but in fact they are divergent near the horizon.

Stability analysis of black holes by the $S$-deformation method for coupled systems · charged squashed Kaluza-Klein black hole · contest 0.72

Builds on it 1 paper

In this paper, we study gravitational and electromagnetic perturbation around the squashed Kaluza-Klein black holes with charge [ref] by extending the analysis in [ref] .

Stability analysis of Squashed Kaluza-Klein Black Holes with Charge · introduction · 1.00

Uses its method or tool 1 paper

SqKK black hole with charge have the $SU(2) ×U(1)$ symmetry as in the neutral case, so we can use the same technics used in [ref] to analyze the perturbations of SqKK black holes with charge.

Stability analysis of Squashed Kaluza-Klein Black Holes with Charge · introduction · 0.95

Compares with it 1 paper

Recently the metric perturbations were discussed [ref] and it was indicated that dynamically the squashed KK black hole is stable, this is consistent with our result.

Quasinormal modes in the background of charged Kaluza-Klein black hole with squashed horizons · Introduction · 0.83

Cites it as support 2 papers

This is even more motivated if we take into account that squashed Kaluza-Klein black holes are gravitationally stable [ref] .

Evolution of perturbations of squashed Kaluza-Klein black holes: escape from instability · Introduction · 0.99
Since the stability for $J=0$ modes is suggested in the limit of both neutral case [ref] and extremal case, and the instability empirically appears in the lower modes, we expect SqKK black holes with charge are stable.

Stability analysis of Squashed Kaluza-Klein Black Holes with Charge · SUMMARY AND DISCUSSION · 0.97

Cites it as background 7 papers

It is known that the equations for gravitational perturbation around a highly symmetric black hole spacetime usually reduce to decoupled master equations [ref] in the form [equation] Using the Fourier transformation with respect to time coordinate, $Φ̃(t,x) = e^-iωtΦ(x)$, the master equation takes the form of the Schrödinger equation [equation] When we wish to prove the stability of the black hole spacetime, we need to show the non-existence of $ω^2 < 0$ solution, i.e., non-existence of exponentially growing solution, under the boundary conditions,[ In this paper, since we mainly focus on asymptotically flat (or de Sitter) black holes, we assume that the range of $x$, which is the tortoise coordinate, is $-∞< x < ∞$.

A simple test for stability of black hole by $S$-deformation · Introduction · 0.99
Several aspects of squashed Kaluza-Klein black holes are also discussed, for example, thermodynamics [ref] , Hawking radiation [ref] , quasinormal modes [ref] , stabilities [ref] , geodetic precession [ref] and strong gravitational lensing [ref] .

Hawking radiation as tunneling from squashed Kaluza-Klein black hole · Introduction · 0.99
In addition, the stability analysis and time domain evolution of perturbations were considered for the Kaluza-Klein type solutions, such as (squashed) Kaluza-Klein black holes [ref] or black strings [ref] .

Gravitational stability of simply rotating Myers-Perry black holes: tensorial perturbations · Introduction · 0.88

What it cites · 8 sentences without a confident label

Uses the method or tool of 1 paper

We explain the formalism to obtain master equations for the metric perturbations [ref] .

A Note on Separability of Field Equations in Myers-Perry Spacetimes · Classification of the metric perturbations based on the symmetry · 0.90

Cites as background 22 papers

The stability analysis of black strings has been done, and it was shown that black strings are stable when the horizon radius is larger than the scale of compact extra dimension [ref] .

Black Strings and p-Branes are Unstable · introduction · 0.85
Interestingly, another possibility has been recognized [ref] .

Kaluza-Klein Black Holes with Squashed Horizons · introduction · 0.80
Related to the stability problem, Bizon et al [ref] investigated the non-liner purtabation of Gross-Perry-Sorkin (GPS) monopole which is the zero mass limit of the SqKK black hole.

Nonlinear perturbations of the Kaluza-Klein monopole · introduction · 0.86

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