pith. sign in

arxiv: 2602.00518 · v1 · pith:FRB6HTUEnew · submitted 2026-01-31 · 🌀 gr-qc

Charged Superradiant Instability of Spherically Symmetric Regular Black Holes in de Sitter Spacetime: Time- and Frequency-Domain Analysis

Yizhi Zhan , Hengyu Xu , Haowei Chen , Shao-Jun Zhang This is my paper

Pith reviewed 2026-05-21 13:54 UTC · model grok-4.3

classification 🌀 gr-qc
keywords superradiant instabilityregular black holesde Sitter spacetimecharged scalar perturbationsnonlinear electrodynamicsABG metrictime-domain evolutionfrequency-domain analysis
0
0 comments X

The pith

de Sitter horizon triggers instability in regular black holes

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper examines how massless charged scalar fields behave around Ayón-Beato-García black holes in de Sitter space. It demonstrates that these regular black holes suffer superradiant instability only in the monopole mode, thanks to the cosmological horizon acting as a confining wall. The growth rate of the instability varies with the cosmological constant, scalar charge, and black hole charge, showing peaks at intermediate values and monotonic increase with charge. This contrasts with the stability of the same black holes in flat spacetime and with the behavior of Reissner-Nordström-de Sitter black holes.

Core claim

Spherically symmetric regular black holes in de Sitter spacetime, described by the Ayón-Beato-García metric from nonlinear electrodynamics, exhibit charged superradiant instability under massless scalar perturbations exclusively for the ℓ=0 mode. The cosmological horizon provides the essential confining boundary that enables the instability, which does not occur in the asymptotically flat limit.

What carries the argument

The ABG-dS metric from nonlinear electrodynamics, whose modified electrostatic potential governs the superradiant condition and produces distinct instability features relative to linear electrodynamics.

If this is right

  • The instability growth rate reaches a maximum at intermediate values of the cosmological constant and scalar charge.
  • The growth rate increases monotonically with increasing black hole charge Q.
  • Only the spherically symmetric ℓ=0 mode is unstable; higher angular modes remain stable.
  • ABG-dS black holes display different instability characteristics from Reissner-Nordström-de Sitter black holes because of the modified electrostatic potential from nonlinear electrodynamics.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The cosmological horizon appears to be the decisive ingredient that turns a stable flat-space configuration into an unstable one for regular black holes.
  • These instabilities may affect the long-term evolution of black holes embedded in expanding cosmologies, potentially sourcing scalar radiation or gravitational-wave signals.
  • Similar analyses for massive scalars or rotating regular black holes could uncover additional instability windows.

Load-bearing premise

The background is fixed as the exact ABG-dS metric from nonlinear electrodynamics while scalar perturbations stay linear, massless, and without back-reaction on the geometry.

What would settle it

A frequency-domain computation or time-domain simulation that finds the imaginary part of the quasinormal frequency negative for every value of Λ, q, and Q in the ℓ=0 sector would falsify the instability.

Figures

Figures reproduced from arXiv: 2602.00518 by Haowei Chen, Hengyu Xu, Shao-Jun Zhang, Yizhi Zhan.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
read the original abstract

We investigate the superradiant instability of Ay\'on-Beato-Garc\'ia-de Sitter (ABG-dS) black holes under massless charged scalar perturbations using both time-domain evolutions and frequency-domain computations. We show that the instability occurs only for the spherically symmetric mode with $\ell=0$, whereas asymptotically flat ABG black holes remain stable in the massless limit, which underscores the essential role of the cosmological horizon in providing a confining boundary. We further study the dependence of the growth rate on the cosmological constant $\Lambda$, the scalar charge $q$, and the black hole charge $Q$, finding that it reaches a maximum at intermediate values of $\Lambda$ and $q$ and increases monotonically with $Q$. Compared with Reissner-Nordstr\"om-de Sitter black holes, ABG-dS black holes exhibit distinct instability characteristics due to the modified electrostatic potential induced by nonlinear electrodynamics.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper investigates charged superradiant instability of Ayón-Beato-García-de Sitter (ABG-dS) regular black holes under massless charged scalar perturbations. Using both time-domain evolutions and frequency-domain quasinormal-mode computations, the authors report that the instability occurs exclusively for the spherically symmetric ℓ=0 mode, while asymptotically flat ABG black holes remain stable in the massless limit. They further examine the dependence of the growth rate on the cosmological constant Λ, scalar charge q, and black-hole charge Q, finding a maximum at intermediate values of Λ and q with monotonic increase in Q, and note distinct characteristics relative to Reissner-Nordström-de Sitter black holes arising from the modified electrostatic potential of nonlinear electrodynamics. The cosmological horizon is identified as providing the essential confining boundary.

Significance. If the numerical results hold, the work demonstrates the essential role of the cosmological horizon in triggering charged superradiant instabilities on regular black-hole backgrounds in de Sitter spacetime, a feature absent in the asymptotically flat case. The dual time- and frequency-domain approach supplies cross-validation, and the explicit parameter scans (maximum growth at intermediate Λ and q, monotonic rise with Q) together with the direct contrast to RN-dS supply concrete, falsifiable predictions. The use of an exact nonlinear-electrodynamics metric rather than an approximate one strengthens the analysis.

major comments (2)
  1. [§4] §4 (time-domain section): the reported growth rates for the ℓ=0 mode rely on direct numerical evolution, yet the manuscript provides no explicit convergence tests, grid-resolution studies, or error estimates on the extracted imaginary parts of the frequencies; these are load-bearing for the central claim that only ℓ=0 is unstable.
  2. [§5] §5 (frequency-domain section): the effective potential for the charged scalar is modified by the nonlinear-electrodynamics term; the manuscript should show explicitly how this modification alters the superradiant condition relative to the RN-dS case (e.g., via a direct comparison of the potential barriers or the critical q/Q ratio).
minor comments (2)
  1. [Abstract] The abstract and introduction use “ABG-dS” without first spelling out the full name on its initial occurrence; this should be corrected for clarity.
  2. [Results] Figure captions for the growth-rate plots should state the precise values of the fixed parameters (e.g., Q=0.5, q=0.3) rather than referring only to “intermediate values.”

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major comment below and will incorporate the suggested improvements in the revised version.

read point-by-point responses

  1. Referee: [§4] §4 (time-domain section): the reported growth rates for the ℓ=0 mode rely on direct numerical evolution, yet the manuscript provides no explicit convergence tests, grid-resolution studies, or error estimates on the extracted imaginary parts of the frequencies; these are load-bearing for the central claim that only ℓ=0 is unstable.

    Authors: We agree that explicit convergence tests, grid-resolution studies, and error estimates are necessary to substantiate the numerical results, particularly given their importance to the claim that instability is restricted to the ℓ=0 mode. In the revised manuscript we will add a new subsection to §4 presenting convergence tests under successive grid refinements, resolution studies, and quantitative error estimates on the extracted imaginary parts of the frequencies. revision: yes

  2. Referee: [§5] §5 (frequency-domain section): the effective potential for the charged scalar is modified by the nonlinear-electrodynamics term; the manuscript should show explicitly how this modification alters the superradiant condition relative to the RN-dS case (e.g., via a direct comparison of the potential barriers or the critical q/Q ratio).

    Authors: We concur that a direct, explicit comparison would clarify how the nonlinear-electrodynamics modification of the electrostatic potential changes the superradiant condition relative to the RN-dS case. In the revised manuscript we will include, in §5, a side-by-side plot of the effective potentials for ABG-dS and RN-dS together with a discussion of the resulting shifts in the critical q/Q ratio and the location of the potential barrier. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's central results on superradiant instability for ℓ=0 modes in ABG-dS spacetime are obtained via direct numerical time-domain evolution of the perturbation equations and frequency-domain quasinormal-mode computations on the exact background metric. These methods solve the linear wave equation without fitting parameters to the target growth rates, without self-referential definitions of the instability criterion, and without load-bearing reliance on prior self-citations that presuppose the present conclusions. The contrast with the asymptotically flat limit follows from the same numerical procedure applied to the Λ=0 case, and the reported parameter dependencies (growth rate vs. Λ, q, Q) are outputs of the computation rather than inputs. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

The analysis rests on the standard Einstein equations coupled to nonlinear electrodynamics for the background metric and on the linear wave equation for a massless charged scalar field; no new entities are postulated.

free parameters (3)
  • Black-hole charge Q
    Physical parameter of the ABG-dS solution that is varied to study instability growth.
  • Cosmological constant Λ
    Parameter controlling the size of the cosmological horizon; varied to locate the maximum growth rate.
  • Scalar charge q
    Charge of the perturbing field; varied to locate the maximum growth rate.
axioms (2)
  • domain assumption The Ayón-Beato-García-de Sitter metric satisfies the Einstein equations sourced by nonlinear electrodynamics.
    Provides the fixed background spacetime on which perturbations are evolved.
  • domain assumption Scalar perturbations remain linear and massless with no back-reaction.
    Justifies the use of the linear wave equation on the fixed metric.

pith-pipeline@v0.9.0 · 5711 in / 1507 out tokens · 51934 ms · 2026-05-21T13:54:47.838246+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

58 extracted references · 58 canonical work pages · 32 internal anchors

  1. [1]

    0.05 0.1 0.15 0.2 0.1111 Q Λ r-=rh rh=r c ABG-dS BH (0.6905,0.1932) FIG

    0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.6341 0. 0.05 0.1 0.15 0.2 0.1111 Q Λ r-=rh rh=r c ABG-dS BH (0.6905,0.1932) FIG. 1. Left: Profile of the metric function f (r) for various Λ, with Q = 0 .3. Right: Allowed region in the Q − Λ plane for which the metric describes a black hole. The two critical curves r− = rh and rh = rc correspond to the two extremal limits. I...

    work page 1932

  2. [2]

    Observation of Gravitational Waves from a Binary Black Hole Merger

    LIGO Scientific, Virgo Collaboration, B. P. Abbott et al. , “Observation of Gravitational Waves from a Binary Black Hole Merger,” Phys. Rev. Lett. 116 no. 6, (2016) 061102 , arXiv:1602.03837 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  3. [3]

    GW151226: Observation of Gravitational Waves from a 22-Solar-Mass Binary Black Hole Coalescence

    LIGO Scientific, Virgo Collaboration, B. P. Abbott et al. , “GW151226: Observation of Gravitational Waves from a 22-Solar-Mass Binary Black Hole Coalescence,” Phys. Rev. Lett. 116 no. 24, (2016) 241103 , arXiv:1606.04855 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  4. [4]

    First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole

    Event Horizon T elescope Collaboration, K. Akiyama et al. , “First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole,” Astrophys. J. Lett. 875 (2019) L1 , arXiv:1906.11238 [astro-ph.GA]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  5. [5]

    First M87 Event Horizon Telescope Results. VI. The Shadow and Mass of the Central Black Hole

    Event Horizon T elescope Collaboration, K. Akiyama et al. , “First M87 Event Horizon Telescope Results. VI. The Shadow and Mass of the Central Black Hole,” Astrophys. J. Lett. 875 no. 1, (2019) 12 L6, arXiv:1906.11243 [astro-ph.GA]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  6. [6]

    Gravitational collapse and space-time singularities,

    R. Penrose, “Gravitational collapse and space-time singularities,” Phys. Rev. Lett. 14 (1965) 57–59

    work page 1965

  7. [7]

    S. W. Hawking and G. F. R. Ellis, The Large Scale Structure of Space-Time . Cambridge Monographs on Mathematical Physics. Cambridge University Press, 2, 2023

    work page 2023

  8. [8]

    Singularity Theorems and Their Consequences

    J. M. M. Senovilla, “Singularity Theorems and Their Consequences,” Gen. Rel. Grav. 30 (1998) 701 , arXiv:1801.04912 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  9. [9]

    Non-singular general relativistic gravitational collapse,

    J. Bardeen, “Non-singular general relativistic gravitational collapse,” in Proceedings of the 5th International Conference on Gravitation and the Theory of Relativity , p. 87. Sept., 1968

    work page 1968

  10. [10]

    Regular Black Hole in General Relativity Coupled to Nonlinear Electrodynamics

    E. Ayón-Beato and A. García, “Regular black hole in general relativity coupled to nonlinear electrodynamics,” Phys. Rev. Lett. 80 no. 23, (1998) 5056–5059 , arXiv:gr-qc/9911046

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  11. [11]

    New Regular Black Hole Solution from Nonlinear Electrodynamics

    E. Ayón-Beato and A. García, “New regular black hole solution from nonlinear electrodynamics,” Physics Letters B 464 no. 1-2, (1999) 25 , arXiv:hep-th/9911174

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  12. [12]

    The Bardeen Model as a Nonlinear Magnetic Monopole

    E. Ayón-Beato and A. García, “The bardeen model as a nonlinear magnetic monopole,” Physics Letters B 493 no. 1-2, (2000) 149–152 , arXiv:gr-qc/0009077

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  13. [13]

    Formation and evaporation of non-singular black holes

    S. A. Hayward, “Formation and evaporation of regular black holes,” Phys. Rev. Lett. 96 (2006) 031103, arXiv:gr-qc/0506126

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  14. [14]

    Vacuum nonsingular black hole,

    I. Dymnikova, “Vacuum nonsingular black hole,” Gen. Rel. Grav. 24 (1992) 235–242

    work page 1992

  15. [15]

    Regular Magnetic Black Holes and Monopoles from Nonlinear Electrodynamics

    K. A. Bronnikov, “Regular magnetic black holes and monopoles from nonlinear electrodynamics,” Phys. Rev. D 63 (2001) 044005 , arXiv:gr-qc/0006014

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  16. [16]

    Regular electrically charged structures in Nonlinear Electrodynamics coupled to General Relativity

    I. Dymnikova, “Regular electrically charged structures in nonlinear electrodynamics coupled to general relativity,” Class. Quant. Grav. 21 (2004) 4417–4429 , arXiv:gr-qc/0407072

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  17. [17]

    Construction of Regular Black Holes in General Relativity

    Z.-Y. Fan and X. Wang, “Construction of Regular Black Holes in General Relativity,” Phys. Rev. D 94 no. 12, (2016) 124027 , arXiv:1610.02636 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  18. [18]

    Regular Black Holes: A Short Topic Review,

    C. Lan, H. Yang, Y. Guo, and Y.-G. Miao, “Regular Black Holes: A Short Topic Review,” Int. J. Theor. Phys. 62 no. 9, (2023) 202 , arXiv:2303.11696 [gr-qc]

    work page arXiv 2023

  19. [19]

    Regular Rotating Black Holes: A Review,

    R. Torres, “Regular Rotating Black Holes: A Review,” arXiv:2208.12713 [gr-qc]

    work page arXiv

  20. [20]

    Regular black holes sourced by nonlinear electrodynamics,

    K. A. Bronnikov, “Regular black holes sourced by nonlinear electrodynamics,” arXiv:2211.00743 [gr-qc]

    work page arXiv

  21. [21]

    Bueno, P.A

    P. Bueno, P. A. Cano, and R. A. Hennigar, “Regular Black Holes From Pure Gravity,” arXiv:2403.04827 [gr-qc]

    work page arXiv

  22. [22]

    Regular hairy black holes through Minkowski deformation,

    J. Ovalle, R. Casadio, and A. Giusti, “Regular hairy black holes through Minkowski deformation,” Phys. Lett. B 844 (2023) 138085 , arXiv:2304.03263 [gr-qc]

    work page arXiv 2023

  23. [23]

    Consequences of Dirac Theory of the Positron

    W. Heisenberg and H. Euler, “Consequences of Dirac’s theory of positrons,” Z. Phys. 98 no. 11-12, (1936) 714–732 , arXiv:physics/0605038

    work page internal anchor Pith review Pith/arXiv arXiv 1936

  24. [24]

    Foundations of the new field theory,

    M. Born and L. Infeld, “Foundations of the new field theory,” Proc. Roy. Soc. Lond. A 144 no. 852, (1934) 425–451

    work page 1934

  25. [25]

    Polchinski, String theory

    J. Polchinski, String theory. Vol. 1: An introduction to the bosonic string . Cambridge Monographs on 13 Mathematical Physics. Cambridge University Press, 12, 2007

    work page 2007

  26. [26]

    Polchinski, String theory

    J. Polchinski, String theory. Vol. 2: Superstring theory and beyond . Cambridge Monographs on Mathematical Physics. Cambridge University Press, 12, 2007

    work page 2007

  27. [27]

    Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant

    Supernova Search T eam Collaboration, A. G. Riess et al. , “Observational evidence from supernovae for an accelerating universe and a cosmological constant,” Astron. J. 116 (1998) 1009–1038, arXiv:astro-ph/9805201

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  28. [28]

    Measurements of Omega and Lambda from 42 High-Redshift Supernovae

    Supernova Cosmology Project Collaboration, S. Perlmutter et al. , “Measurements of Ω and Λ from 42 High Redshift Supernovae,” Astrophys. J. 517 (1999) 565–586 , arXiv:astro-ph/9812133

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  29. [29]

    Planck 2018 results. VI. Cosmological parameters

    Planck Collaboration, N. Aghanim et al. , “Planck 2018 results. VI. Cosmological parameters,” Astron. Astrophys. 641 (2020) A6 , arXiv:1807.06209 [astro-ph.CO] . [Erratum: Astron.Astrophys. 652, C4 (2021)]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  30. [30]

    Cosmological Event Horizons, Thermodynamics, and Particle Creation,

    G. W. Gibbons and S. W. Hawking, “Cosmological Event Horizons, Thermodynamics, and Particle Creation,” Phys. Rev. D 15 (1977) 2738–2751

    work page 1977

  31. [31]

    Telling Tails In The Presence Of A Cosmological Constant

    P. R. Brady, C. M. Chambers, W. Krivan, and P. Laguna, “Telling tails in the presence of a cosmological constant,” Phys. Rev. D 55 (1997) 7538–7545 , arXiv:gr-qc/9611056

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  32. [32]

    Radiative falloff in Schwarzschild-de Sitter spacetime

    P. R. Brady, C. M. Chambers, W. G. Laarakkers, and E. Poisson, “Radiative falloff in Schwarzschild-de Sitter space-time,” Phys. Rev. D 60 (1999) 064003 , arXiv:gr-qc/9902010

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  33. [33]

    Field propagation in de Sitter black holes

    C. Molina, D. Giugno, E. Abdalla, and A. Saa, “Field propagation in de Sitter black holes,” Phys. Rev. D 69 (2004) 104013 , arXiv:gr-qc/0309079

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  34. [34]

    Quasinormal modes of Schwarzschild black holes in four and higher dimensions

    V. Cardoso, J. P. S. Lemos, and S. Yoshida, “Quasinormal modes of Schwarzschild black holes in four-dimensions and higher dimensions,” Phys. Rev. D 69 (2004) 044004 , arXiv:gr-qc/0309112

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  35. [35]

    Stability of Reissner-Nordstr\"om black hole in de Sitter background under charged scalar perturbation

    Z. Zhu, S.-J. Zhang, C. E. Pellicer, B. Wang, and E. Abdalla, “Stability of Reissner-Nordström black hole in de Sitter background under charged scalar perturbation,” Phys. Rev. D 90 no. 4, (2014) 044042, arXiv:1405.4931 [hep-th] . [Addendum: Phys.Rev.D 90, 049904 (2014)]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  36. [36]

    Charged scalar field instability between the event and cosmological horizons

    R. A. Konoplya and A. Zhidenko, “Charged scalar field instability between the event and cosmological horizons,” Phys. Rev. D 90 no. 6, (2014) 064048 , arXiv:1406.0019 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  37. [37]

    On Quantum Resonances in Stationary Geometries,

    T. Damour, N. Deruelle, and R. Ruffini, “On Quantum Resonances in Stationary Geometries,” Lett. Nuovo Cim. 15 (1976) 257–262

    work page 1976

  38. [38]

    KLEIN-GORDON EQUATION AND ROTATING BLACK HOLES,

    S. L. Detweiler, “KLEIN-GORDON EQUATION AND ROTATING BLACK HOLES,” Phys. Rev. D 22 (1980) 2323–2326

    work page 1980

  39. [39]

    INSTABILITIES OF MASSIVE SCALAR PERTURBATIONS OF A ROTATING BLACK HOLE,

    T. J. M. Zouros and D. M. Eardley, “INSTABILITIES OF MASSIVE SCALAR PERTURBATIONS OF A ROTATING BLACK HOLE,” Annals Phys. 118 (1979) 139–155

    work page 1979

  40. [40]

    Superradiant instabilities of rotating black branes and strings

    V. Cardoso and S. Yoshida, “Superradiant instabilities of rotating black branes and strings,” JHEP 07 (2005) 009 , arXiv:hep-th/0502206

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  41. [41]

    Instability of the massive Klein-Gordon field on the Kerr spacetime

    S. R. Dolan, “Instability of the massive Klein-Gordon field on the Kerr spacetime,” Phys. Rev. D 76 (2007) 084001 , arXiv:0705.2880 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  42. [42]

    A massive charged scalar field in the Kerr-Newman background I: quasinormal modes, late-time tails and stability

    R. A. Konoplya and A. Zhidenko, “Massive charged scalar field in the Kerr-Newman background I: 14 quasinormal modes, late-time tails and stability,” Phys. Rev. D 88 (2013) 024054 , arXiv:1307.1812 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  43. [43]

    No-bomb theorem for charged Reissner-Nordstrom black holes

    S. Hod, “Stability of the extremal Reissner-Nordstroem black hole to charged scalar perturbations,” Phys. Lett. B 713 (2012) 505–508 , arXiv:1304.6474 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  44. [44]

    No-bomb theorem for charged Reissner-Nordstroem black holes,

    S. Hod, “No-bomb theorem for charged Reissner-Nordstroem black holes,” Phys. Lett. B 718 (2013) 1489–1492

    work page 2013

  45. [45]

    Rapid growth of superradiant instabilities for charged black holes in a cavity

    C. A. R. Herdeiro, J. C. Degollado, and H. F. Rúnarsson, “Rapid growth of superradiant instabilities for charged black holes in a cavity,” Phys. Rev. D 88 (2013) 063003 , arXiv:1305.5513 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  46. [46]

    Stability of black holes in Einstein-charged scalar field theory in a cavity

    S. R. Dolan, S. Ponglertsakul, and E. Winstanley, “Stability of black holes in Einstein-charged scalar field theory in a cavity,” Phys. Rev. D 92 no. 12, (2015) 124047 , arXiv:1507.02156 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  47. [47]

    Charged black hole bombs in a Minkowski cavity

    O. J. C. Dias and R. Masachs, “Charged black hole bombs in a Minkowski cavity,” Class. Quant. Grav. 35 no. 18, (2018) 184001 , arXiv:1801.10176 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  48. [48]

    Phase diagram of the charged black hole bomb system,

    A. Davey, O. J. C. Dias, and P. Rodgers, “Phase diagram of the charged black hole bomb system,” JHEP 05 (2021) 189 , arXiv:2103.12752 [gr-qc]

    work page arXiv 2021

  49. [49]

    Scattering and absorption of a scalar field impinging on a charged black hole in the Einstein-Maxwell-dilaton theory,

    M. G. Richarte, E. L. Martins, and J. C. Fabris, “Scattering and absorption of a scalar field impinging on a charged black hole in the Einstein-Maxwell-dilaton theory,” Phys. Rev. D 105 no. 6, (2022) 064043 , arXiv:2111.01595 [gr-qc]

    work page arXiv 2022

  50. [50]

    Penrose process in Reissner-Nordström-AdS black hole spacetimes: Black hole energy factories and black hole bombs,

    D. Feiteira, J. P. S. Lemos, and O. B. Zaslavskii, “Penrose process in Reissner-Nordström-AdS black hole spacetimes: Black hole energy factories and black hole bombs,” Phys. Rev. D 109 no. 6, (2024) 064065, arXiv:2401.13039 [gr-qc]

    work page arXiv 2024

  51. [51]

    Spatially regular charged black holes supporting charged massive scalar clouds,

    S. Hod, “Spatially regular charged black holes supporting charged massive scalar clouds,” Phys. Rev. D 109 no. 6, (Mar., 2024) 064074 , arXiv:2401.07907 [gr-qc]

    work page arXiv 2024

  52. [52]

    Absorption and (unbounded) superradiance in a static regular black hole spacetime,

    M. A. A. de Paula, L. C. S. Leite, S. R. Dolan, and L. C. B. Crispino, “Absorption and (unbounded) superradiance in a static regular black hole spacetime,” arXiv:2401.01767 [gr-qc]

    work page arXiv

  53. [53]

    Superradiant instability of a charged regular black hole,

    S. R. Dolan, M. A. A. de Paula, L. C. S. Leite, and L. C. B. Crispino, “Superradiant instability of a charged regular black hole,” Phys. Rev. D 109 no. 12, (June, 2024) 124037 , arXiv:2401.14967 [gr-qc]

    work page arXiv 2024

  54. [54]

    Regular black holes with cosmological constant,

    W.-J. Mo, R.-G. Cai, and R.-K. Su, “Regular black holes with cosmological constant,” Commun. Theor. Phys. 46 (2006) 453–460

    work page 2006

  55. [55]

    Phase transitions and regions of stability in Reissner-Nordstr\"om holographic superconductors

    E. Abdalla, C. E. Pellicer, J. de Oliveira, and A. B. Pavan, “Phase transitions and regions of stability in Reissner-Nordström holographic superconductors,” Phys. Rev. D 82 (2010) 124033 , arXiv:1010.2806 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  56. [56]

    Advanced Methods in Black-Hole Perturbation Theory

    P. Pani, “Advanced Methods in Black-Hole Perturbation Theory,” Int. J. Mod. Phys. A 28 (2013) 1340018, arXiv:1305.6759 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  57. [57]

    Charged superradiant instability in a spherical regular black hole,

    Y. Zhan, H. Xu, and S.-J. Zhang, “Charged superradiant instability in a spherical regular black hole,” Eur. Phys. J. C 84 no. 12, (2024) 1315 , arXiv:2410.19261 [gr-qc]

    work page arXiv 2024

  58. [58]

    Superradiance -- the 2020 Edition

    R. Brito, V. Cardoso, and P. Pani, “Superradiance: New Frontiers in Black Hole Physics,” Lect. Notes 15 Phys. 906 (2015) pp.1–237 , arXiv:1501.06570 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2015