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Classical stability of black holes under massless Dirac perturbations
General Relativity and Quantum Cosmology · Submitted 8 Nov 2012
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Here with the help of the S-deformation method, we state their classical stability against the massless Dirac field, extend these results to maximally symmetric black holes, and comment on the applicability of our results to establish the stability with respect to other classical fields.
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The abstract, sentence by sentence
In a D-dimensional maximally symmetric spacetime we simplify the massless Dirac equation to two decoupled wavelike equations with effective potentials. Furthermore in D-dimensional Schwarzschild and Schwarzschild de Sitter black holes we note that for the massless Dirac field moving in the region exterior to the event horizon at least one of the effective potentials is not positive definite. Therefore the classical stability of these black holes against this field is not guaranteed. Here with the help of the S-deformation method, we state their classical stability against the massless Dirac field, extend these results to maximally symmetric black holes, and comment on the applicability of our results to establish the stability with respect to other classical fields.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In a D-dimensional maximally symmetric spacetime we simplify the massless Dirac equation to two decoupled wavelike equations with effective potentials. | method 0.82 | 0.86 | 0.04 | asserted 1.00 |
| s1 | Furthermore in D-dimensional Schwarzschild and Schwarzschild de Sitter black holes we note that for the massless Dirac field moving in the region exterior to the event horizon at least one of the effective potentials is not positive definite. | result 0.99 | 0.82 | 0.11 | asserted 0.97 |
| s2 | Therefore the classical stability of these black holes against this field is not guaranteed. | interpretation 0.71 | 0.62 | 0.23 | asserted 0.82 |
| s3 | Here with the help of the S-deformation method, we state their classical stability against the massless Dirac field, extend these results to maximally symmetric black holes, and comment on the applicability of our results to establish the stability with respect to other classical fields. | contribution 1.00 | 0.94 | 0.77 | asserted 1.00 |
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The paper
Original abstract
In a D-dimensional maximally symmetric spacetime we simplify the massless Dirac equation to two decoupled wavelike equations with effective potentials. Furthermore in D-dimensional Schwarzschild and Schwarzschild de Sitter black holes we note that for the massless Dirac field moving in the region exterior to the event horizon at least one of the effective potentials is not positive definite. Therefore the classical stability of these black holes against this field is not guaranteed. Here with the help of the S-deformation method, we state their classical stability against the massless Dirac field, extend these results to maximally symmetric black holes, and comment on the applicability of our results to establish the stability with respect to other classical fields.
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How the literature uses it
6 arXiv papers cite this in 10 sentences
Papers citing it · 6 sentences without a confident label
Uses its method or tool 3 papers
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Appropriate functions are given by $S=-W$ for $V_+$ and $S=W$ for $V_-$ [ref] , [ref] .
Fermionic field perturbations of a three-dimensional Lifshitz black hole in conformal gravity · Stability analysis · 0.90
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Appropriate functions are given by $S=-W$ for $V_+$ and $S=W$ for $V_-$ [ref] .
Perturbative and nonperturbative fermionic quasinormal modes of Einstein-Gauss-Bonnet-AdS black holes · Stability of massless fermionic field · 0.95
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To ensure the stability of the spacetime against the perturbation field, a $S(ρ)$ function needs to be found such that the new potential satisfies $Ṽ_1≥0$ [ref] .
Quasinormal modes of three $(2+1)$-dimensional black holes in string theory, conformal gravity, and Hu-Sawicki $F(R)$ theory via the Heun function · Stability analysis · 0.99
What it cites · 23 sentences without a confident label
Uses the method or tool of 2 papers
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To show that the operators $A_±$ of the formula ([ref]) can be extended to positive self-adjoint operators we use the $S$-deformation method [ref] – [ref] .
Perturbations and Stability of Static Black Holes in Higher Dimensions · Stability analysis · 1.00
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To show that the operators $A_±$ of the formula ([ref]) can be extended to positive self-adjoint operators we use the $S$-deformation method [ref] – [ref] .
Stability of Higher-Dimensional Schwarzschild Black Holes · Stability analysis · 1.00
Compares with 2 papers
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For the $D$-dimensional Reissner-Nordström de Sitter spacetime our result about its classical stability with respect to massless Dirac perturbations is different from that of Ref. [ref] (see also Ref. [ref] ) since for $D ≥7$ this black hole is unstable under the coupled electromagnetic and gravitational perturbations of scalar type [ref] .
Instability of higher dimensional charged black holes in the de-Sitter world · Generalization · 0.95
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For the $D$-dimensional Reissner-Nordström de Sitter spacetime our result about its classical stability with respect to massless Dirac perturbations is different from that of Ref. [ref] (see also Ref. [ref] ) since for $D ≥7$ this black hole is unstable under the coupled electromagnetic and gravitational perturbations of scalar type [ref] .
On the instability of Reissner-Nordstrom black holes in de Sitter backgrounds · Generalization · 0.95
Cites as background 6 papers
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The analysis of the dynamics of the classical fields in black hole spacetimes is necessary to calculate significant physical quantities and in the study of relevant physical phenomena [ref] – [ref] , for example, by investigating the dynamics of perturbing fields we can determine the classical stability of the black holes with respect to linear perturbations [ref] – [ref] .
Quasinormal modes of black holes: from astrophysics to string theory · Introduction · 0.96
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The analysis of the dynamics of the classical fields in black hole spacetimes is necessary to calculate significant physical quantities and in the study of relevant physical phenomena [ref] – [ref] , for example, by investigating the dynamics of perturbing fields we can determine the classical stability of the black holes with respect to linear perturbations [ref] – [ref] .
Quasi-Normal Modes of Stars and Black Holes · Introduction · 0.96
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The analysis of the dynamics of the classical fields in black hole spacetimes is necessary to calculate significant physical quantities and in the study of relevant physical phenomena [ref] – [ref] , for example, by investigating the dynamics of perturbing fields we can determine the classical stability of the black holes with respect to linear perturbations [ref] – [ref] .
On the instability of Reissner-Nordstrom black holes in de Sitter backgrounds · Introduction · 0.96
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