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Hunting for fermionic instabilities in charged AdS black holes
High Energy Physics - Theory · Submitted 9 Oct 2019
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Motivated by this observation we search for linear mode instabilities of Dirac fields in these backgrounds but find none.
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The abstract, sentence by sentence
Fermions scattering on a black hole background cannot develop an instability sourced by superradiance. However, in a global (or planar) AdS$_4$-Reissner-Nordstr\"om background fermions can violate the AdS$_2$ fermionic mass stability bound as measured by a near horizon observer at zero temperature. This suggests that AdS-Reissner-Nordstr\"om black holes might still be unstable to Dirac perturbations. Motivated by this observation we search for linear mode instabilities of Dirac fields in these backgrounds but find none. This is in contrast with the scalar field case, where a violation of the near-horizon Breitenl\"ohner-Freedman stability bound in the AdS-Reissner-Nordstr\"om background triggers the already known scalar condensation near-horizon linear instability (in the planar limit this is Gubser's instability that initiated the holographic superconductor programme). We consider both the standard and alternative AdS/CFT quantizations (that preserve the conformal invariance of AdS). These are reflective boundary conditions that have vanishing energy flux at the asymptotic boundary.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Fermions scattering on a black hole background cannot develop an instability sourced by superradiance. | background 0.91 | 0.15 | 0.15 | asserted 1.00 |
| s1 | However, in a global (or planar) AdS$_4$-Reissner-Nordstr\"om background fermions can violate the AdS$_2$ fermionic mass stability bound as measured by a near horizon observer at zero temperature. | result 0.73 | 0.47 | 0.05 | asserted 0.97 |
| s2 | This suggests that AdS-Reissner-Nordstr\"om black holes might still be unstable to Dirac perturbations. | interpretation 0.93 | 0.20 | 0.05 | hedged possibility 0.84 |
| s3 | Motivated by this observation we search for linear mode instabilities of Dirac fields in these backgrounds but find none. | result 0.98 | 0.96 | 0.80 | asserted 1.00 |
| s4 | This is in contrast with the scalar field case, where a violation of the near-horizon Breitenl\"ohner-Freedman stability bound in the AdS-Reissner-Nordstr\"om background triggers the already known scalar condensation near-horizon linear instability (in the planar limit this is Gubser's instability that initiated the holographic superconductor programme). | background 0.45 | 0.18 | 0.16 | asserted 1.00 |
| s5 | We consider both the standard and alternative AdS/CFT quantizations (that preserve the conformal invariance of AdS). | method 0.91 | 0.81 | 0.02 | asserted 0.93 |
| s6 | These are reflective boundary conditions that have vanishing energy flux at the asymptotic boundary. | method 0.95 | 0.27 | 0.02 | asserted 1.00 |
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The paper
Original abstract
Fermions scattering on a black hole background cannot develop an instability sourced by superradiance. However, in a global (or planar) AdS$_4$-Reissner-Nordstr\"om background fermions can violate the AdS$_2$ fermionic mass stability bound as measured by a near horizon observer at zero temperature. This suggests that AdS-Reissner-Nordstr\"om black holes might still be unstable to Dirac perturbations. Motivated by this observation we search for linear mode instabilities of Dirac fields in these backgrounds but find none. This is in contrast with the scalar field case, where a violation of the near-horizon Breitenl\"ohner-Freedman stability bound in the AdS-Reissner-Nordstr\"om background triggers the already known scalar condensation near-horizon linear instability (in the planar limit this is Gubser's instability that initiated the holographic superconductor programme). We consider both the standard and alternative AdS/CFT quantizations (that preserve the conformal invariance of AdS). These are reflective boundary conditions that have vanishing energy flux at the asymptotic boundary.
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How the literature uses it
5 arXiv papers cite this in 6 sentences
What it cites · 215 sentences without a confident label
Contests 12 papers
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To complete the spectrum of Schwarzschild-AdS (and global AdS) note that frequencies that are the negative of the complex conjugate of the frequencies ($-ω^*$) plotted in Fig. [ref] are also eigenvalues of the system (which was missed in [ref] ).
Dirac perturbations on Schwarzschild-Anti-de Sitter spacetimes: Generic boundary conditions and new quasinormal modes · Comparing numerical results with analytical expansions · contest 0.90
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Namely, the authors of [ref] [See also Ref. [ref] , which appeared after the present manuscript was submitted to the ArXiv.] missed that the vanishing energy flux boundary conditions at the asymptotic boundary of AdS $-$ that they propose to be “novel" $-$ are nothing else but the AdS/CFT correspondence no-source boundary conditions $-$ often denoted as `standard' or, if allowed, `alternative' quantizations (discussed, for $s=1/2$, originally in [ref] and specially in [ref] ; this discussion applies both to bosonic and fermionic fields).
String Theory, Quantum Phase Transitions and the Emergent Fermi-Liquid · Introduction · contest 0.91
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Namely, the authors of [ref] [See also Ref. [ref] , which appeared after the present manuscript was submitted to the ArXiv.] missed that the vanishing energy flux boundary conditions at the asymptotic boundary of AdS $-$ that they propose to be “novel" $-$ are nothing else but the AdS/CFT correspondence no-source boundary conditions $-$ often denoted as `standard' or, if allowed, `alternative' quantizations (discussed, for $s=1/2$, originally in [ref] and specially in [ref] ; this discussion applies both to bosonic and fermionic fields).
Charged Dirac perturbations on Reissner-Nordstr\"om-Anti-de Sitter spacetimes: quasinormal modes with Robin boundary conditions · Introduction · contest 0.91
Uses the method or tool of 12 papers
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In this section we derive an analytical expression for the imaginary part of the Dirac frequency using the method of matched asymptotic expansion introduced in [ref] (see also e.g. [ref] ).
Small Kerr-anti-de Sitter black holes are unstable · Matched asymptotic expansion · 1.00
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In this section we derive an analytical expression for the imaginary part of the Dirac frequency using the method of matched asymptotic expansion introduced in [ref] (see also e.g. [ref] ).
The black hole bomb and superradiant instabilities · Matched asymptotic expansion · 1.00
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To arrive to this conclusion we first use a matching asymptotic expansion similar to the one used in de Sitter [ref] to find the frequency spectrum of the near-extremal family of quasinormal modes.
Strong cosmic censorship in de Sitter space · Scalar fields in a AdS-RN background and their instabilities · 0.96
Uses data or values from 1 paper
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This result is taken from [ref] (we already mentioned it to get the bound [ref]): [equation] where $e=q L$.
Hairy black holes and the endpoint of AdS$_4$ charged superradiance · Scalar fields in a AdS-RN background and their instabilities · 0.94
Compares with 9 papers
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Our stability results are also consistent with the stability study of fermions in planar AdS, where no instability was found [ref] (see also [ref] ).[This sharp difference between the stability conclusion of scalar and Dirac fields in RN-AdS is probably due to the fact that the Dirac equation is originally a first order PDE.
Holographic Fermi surfaces and bulk dipole couplings · Discussion and conclusions · 0.86
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Our stability results are also consistent with the stability study of fermions in planar AdS, where no instability was found [ref] (see also [ref] ).[This sharp difference between the stability conclusion of scalar and Dirac fields in RN-AdS is probably due to the fact that the Dirac equation is originally a first order PDE.
A Non-Fermi Liquid from a Charged Black Hole; A Critical Fermi Ball · Discussion and conclusions · 0.86
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Our stability results are also consistent with the stability study of fermions in planar AdS, where no instability was found [ref] (see also [ref] ).[This sharp difference between the stability conclusion of scalar and Dirac fields in RN-AdS is probably due to the fact that the Dirac equation is originally a first order PDE.
Non-Fermi liquids from holography · Discussion and conclusions · 0.86
Cites as support 1 paper
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If and only if this is the case, the Schrödinger operator that describes the (bosonic or fermionic) wave equation in AdS is Hermitian[Without the zero flux or energy conservation condition, the Schröedinger operator is only symmetric [ref] .].
Dynamics in Non-Globally-Hyperbolic Static Spacetimes III: Anti-de Sitter Spacetime · Introduction · 0.96
Cites as background 11 papers
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We do not discuss further this special case (see [ref] for more details).
Real-time response in AdS/CFT with application to spinors · Dirac equation in the AdS-RN background · 0.93
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We do not discuss further this special case (see [ref] for more details).
Supersymmetric Multi-trace Boundary Conditions in AdS · Dirac equation in the AdS-RN background · 0.93
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Typically, such extreme black holes have a near-horizon geometry that is the direct product (or a fibration) of a base space (e.g. a sphere) and an AdS$_2$ space [ref] .
The Extreme Kerr Throat Geometry: A Vacuum Analog of AdS_2 x S^2 · Introduction · 0.82
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