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Cited by 2Black Holes and Theoretical PhysicsCosmology and Gravitation TheoriesParticle physics theoretical and experimental studies

The DOI matches its Crossref record; 69 of the 69 references it cites were found in a registry or an index; none of the 13 sources its claims cite is checked for support yet.

Vacuum decay and bubble nucleation in the anti-de Sitter black holes

Open access
Li, Ran, Wang, Jin·2022·Journal of High Energy Physics
DOI 10.1007/jhep09(2022)151
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Abstract

We study the vacuum decay and the bubble nucleation in the anti-de Sitter black holes. In the bubble nucleation spacetime, the interior and the exterior of the bubble wall are described by two anti-de Sitter black hole spacetimes with different cosmological constants. We calculate the Euclidean action of the bubble nucleation spacetime and give the numerical results of the tunneling rates for different cases. It is shown that the black hole can act as a source of inhomogeneities and catalyze the vacuum decay and the bubble nucleation in the anti-de Sitter spacetime. For the RNAdS black holes, the tunneling rate to the final RNAdS black hole with the minimum critical mass is the highest among all the possible tunneling channels.

Overview

AI snapshot

Written from the paper’s full text.

TL;DR

The paper studies false-vacuum decay and bubble nucleation seeded by anti-de Sitter black holes, using a thin-wall Euclidean bounce formalism with interior and exterior RNAdS spacetimes. It finds that black holes can catalyze vacuum decay, and for RNAdS black holes the highest tunneling rate is to the final black hole with the minimum critical mass.

Key findings

  • Black holes can act as sources of inhomogeneity and catalyze bubble nucleation in AdS spacetime; the numerical tunneling coefficient \(B/B_{\rm CDL}\) reproduces the Coleman–De Luccia result as \(M_+\to 0\) and \(B\) decreases as the seed black hole mass increases, so the rate \(\Gamma \propto e^{-B}\) increases.
  • For Schwarzschild AdS black holes, a Euclidean bounce exists only for initial black hole masses below a critical mass; the paper reports \(M_c=0.0863\) for \(G=1\), \(L_+=1.4\), \(L_-=1\), \(\sigma=1/(16\pi G)\).
  • For RNAdS black holes, with fixed initial mass there is a minimum critical final mass allowing a bounce; the paper reports \(M_c=0.4794\) for \(G=1\), \(L_+=1.335\), \(L_-=1\), \(\sigma=1/(16\pi G)\), \(Q=0.3\), \(M_+=1\). The tunneling coefficient increases with final mass, so the rate to the minimum critical mass is highest.
  • Necessary conditions for the Euclidean bounce include non-extremal interior/exterior RNAdS black holes and \(\Delta>1\); for the special case \(D=0\), the electric charge \(Q\) is restricted.

Methods

  • The spacetime is split by an uncharged thin wall into two RNAdS regions with different cosmological constants; the wall trajectory is derived from the Israel junction conditions, with the SAdS case obtained by setting \(Q=0\).
  • After Wick rotation, the Euclidean equation of motion for the bubble wall is obtained, and the existence conditions for the bounce solution are analyzed in terms of the black hole masses, charges, AdS radii, and wall tension.
  • The Euclidean action is calculated analytically where possible, and the tunneling coefficient \(B=I_E-I_B\) is evaluated numerically for Schwarzschild, SAdS, and RNAdS cases; the semiclassical rate is \(\Gamma \propto e^{-B}\).

Limitations

  • The paper states that the thin wall model considered is uncharged, whereas a bubble wall in a charged spacetime background should generally be charged; it lists charged thin walls and higher-derivative/modified gravity as future directions.
  • The paper states that the analytical derivation of the Euclidean action can only reach a certain result and that the tunneling coefficient can only be calculated numerically.
  • Evident from the text: the numerical results depend on chosen parameter values in the figures, and no observational or experimental data are used.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.1007/jhep09(2022)151

Cites

69 of 69 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Verification

Claims the paper makes

0 of 13 cited sources checked · 0 supported · 0 flagged

  • Findingown data

    The tunneling coefficient is an increasing function of the final black hole mass.

    “It is shown that the tunneling coefficient is the increasing function of the final black hole mass.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The bubble wall is uncharged.
    • The authors state this as an assumption: The energy-momentum tensor of the wall is S_ab = -σ h_ab, where σ is the tension of the wall.
    • The authors state this as an assumption: The vacuum energy of the interior spacetime is smaller than that of the exterior spacetime, i.e. L+ > L-.
    • The authors state this as an assumption: The bubble nucleation has O(3) symmetry.
    • The authors state this as an assumption: The bubble wall is thin.
  • Findingown data

    The numerical result perfectly reproduces the CDL result at the limit M+ → 0.

    “Our numerical result perfectly reproduces the CDL result at the limit M + → 0.”
    • Also stated in: § 6 Conclusion · plain
      “It is found that the numerical result perfectly reproduce the CDL's result when the mass of the initial Schwarzschild black hole approaches zero.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [14] S.R. Coleman and F. De Luccia, Gravitational Effects on and of Vacuum Decay, Phys. Rev. D 21 (1980) 3305 [INSPIRE]. source
    • The authors state this as an assumption: The bubble wall is uncharged.
    • The authors state this as an assumption: The energy-momentum tensor of the wall is S_ab = -σ h_ab, where σ is the tension of the wall.
    • The authors state this as an assumption: The vacuum energy of the interior spacetime is smaller than that of the exterior spacetime, i.e. L+ > L-.
    • The authors state this as an assumption: The bubble nucleation has O(3) symmetry.
    • The authors state this as an assumption: The bubble wall is thin.
  • Findingcitation

    The existence condition of the bounce solution in the SAdS case is Δ > 1, consistent with [5,6].

    “The existence condition of the bounce solution in this case is ∆ > 1, which is consistent with the condition given in [5,6].”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [5] M. Sasaki and D.-h. Yeom, Thin-shell bubbles and information loss problem in anti de Sitter background, JHEP 12 (2014) 155 [arXiv:1404.1565] [INSPIRE]. source
    • cites [6] P. Chen, G. Domènech, M. Sasaki and D.-h. Yeom, Thermal activation of thin-shells in anti-de Sitter black hole spacetime, JHEP 07 (2017) 134 [arXiv:1704.04020] [INSPIRE]. source
    • The authors state this as an assumption: The bubble wall is uncharged.
    • The authors state this as an assumption: The energy-momentum tensor of the wall is S_ab = -σ h_ab, where σ is the tension of the wall.
    • The authors state this as an assumption: The vacuum energy of the interior spacetime is smaller than that of the exterior spacetime, i.e. L+ > L-.
    • The authors state this as an assumption: The bubble nucleation has O(3) symmetry.
    • The authors state this as an assumption: The bubble wall is thin.
  • Findingnone given

    For a fixed mass of the exterior (initial) RNAdS black hole, there exists a minimum mass of the interior (final) RNAdS black hole that the bounce solution exists.

    “It is also shown that for the fixed mass of the exterior (initial) RNAdS black hole, there exists a minimum mass of the interior (final) RNAdS black hole that the bounce solution exists.”
    • Also stated in: § 6 Conclusion · plain
      “It is also shown that for the fixed mass of the exterior (initial) RNAdS black hole, there exists a minimum mass of the interior (final) RNAdS black hole that the bounce solution exists.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The bubble wall is uncharged.
    • The authors state this as an assumption: The energy-momentum tensor of the wall is S_ab = -σ h_ab, where σ is the tension of the wall.
    • The authors state this as an assumption: The vacuum energy of the interior spacetime is smaller than that of the exterior spacetime, i.e. L+ > L-.
    • The authors state this as an assumption: The bubble nucleation has O(3) symmetry.
    • The authors state this as an assumption: The bubble wall is thin.
  • Findingcitation

    The semiclassical tunneling rate is Γ ∝ e^{-B}.

    “The semiclassical tunneling rate is then given by [12,13] Γ ∝ e -B .”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [12] S.R. Coleman, The Fate of the False Vacuum. 1. Semiclassical Theory, Phys. Rev. D 15 (1977) 2929 [Erratum ibid. 16 (1977) 1248] [INSPIRE]. source
    • cites [13] C.G. Callan, Jr. and S.R. Coleman, The Fate of the False Vacuum. 2. First Quantum Corrections, Phys. Rev. D 16 (1977) 1762 [INSPIRE]. source
    • The authors state this as an assumption: The bubble wall is uncharged.
    • The authors state this as an assumption: The energy-momentum tensor of the wall is S_ab = -σ h_ab, where σ is the tension of the wall.
    • The authors state this as an assumption: The vacuum energy of the interior spacetime is smaller than that of the exterior spacetime, i.e. L+ > L-.
    • The authors state this as an assumption: The bubble nucleation has O(3) symmetry.
    • The authors state this as an assumption: The bubble wall is thin.
  • It may state two separate claims as one. 4
  • Probably not a substantial claim. 3

  • It may state two separate claims as one.

    Findingown data

    In RNAdS, increasing the mass M+ will decrease the tunneling coefficient B, which in turn will increase the tunneling rate of the bounce solution.

    “It is shown that increasing the mass M + will decrease the tunneling coefficient B, which in turn will increase the tunneling rate of the bounce solution.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The bubble wall is uncharged.
    • The authors state this as an assumption: The energy-momentum tensor of the wall is S_ab = -σ h_ab, where σ is the tension of the wall.
    • The authors state this as an assumption: The vacuum energy of the interior spacetime is smaller than that of the exterior spacetime, i.e. L+ > L-.
    • The authors state this as an assumption: The bubble nucleation has O(3) symmetry.
    • The authors state this as an assumption: The bubble wall is thin.

  • It may state two separate claims as one.

    Findingown data

    In the SAdS black hole, there is a critical mass Mc of the initial black hole; when 0 < M+ < Mc, there exists the Euclidean bounce solution; when M+ > Mc, there is no intersection.

    “It is shown that there is a critical mass M c of the initial black hole.When M + = M c , the potential curve is tangent to the R-axial.When 0 < M + < M c , there exists the Euclidean bounce solution.”
    • Also stated in: § 6 Conclusion · plain
      “The critical black hole mass is M c = 0.0863.When 0 < M + < M c , the effective potential has two intersections with the R axial.When M + > M c , there is no intersection.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The bubble wall is uncharged.
    • The authors state this as an assumption: The energy-momentum tensor of the wall is S_ab = -σ h_ab, where σ is the tension of the wall.
    • The authors state this as an assumption: The vacuum energy of the interior spacetime is smaller than that of the exterior spacetime, i.e. L+ > L-.
    • The authors state this as an assumption: The bubble nucleation has O(3) symmetry.
    • The authors state this as an assumption: The bubble wall is thin.

  • It may state two separate claims as one.

    Findingreasoning

    The necessary conditions for the existence of a Euclidean bounce solution are that the interior/exterior RNAdS black hole is non-extremal and that Δ > 1.

    “In summary, the necessary conditions for the existence of Euclidean bounce solution are (1) the interior/exterior RNAdS black hole is non-extremal; (2) ∆ > 1.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The bubble wall is uncharged.
    • The authors state this as an assumption: The energy-momentum tensor of the wall is S_ab = -σ h_ab, where σ is the tension of the wall.
    • The authors state this as an assumption: The vacuum energy of the interior spacetime is smaller than that of the exterior spacetime, i.e. L+ > L-.
    • The authors state this as an assumption: The bubble nucleation has O(3) symmetry.
    • The authors state this as an assumption: The bubble wall is thin.

  • It may state two separate claims as one.

    Findingreasoning

    The tunneling coefficient B depends on the bounce solution, which is only solved numerically.

    “This result indicates that the tunneling coefficient B depends on the bounce solution, which is only solved numerically.”
    Quote in the paperNot a substantial claim
    • The authors state this as an assumption: The bubble wall is uncharged.
    • The authors state this as an assumption: The energy-momentum tensor of the wall is S_ab = -σ h_ab, where σ is the tension of the wall.
    • The authors state this as an assumption: The vacuum energy of the interior spacetime is smaller than that of the exterior spacetime, i.e. L+ > L-.
    • The authors state this as an assumption: The bubble nucleation has O(3) symmetry.
    • The authors state this as an assumption: The bubble wall is thin.

  • Probably not a substantial claim.

    Premisecitation

    When the transition is spatially homogeneous, the dynamics of the RNAdS black hole phase transition has been studied based on the underlying free energy landscape.

    “When the transition is spatial homogeneous, the dynamics of the RNAdS black hole phase transition has been studied based on the underlying free energy landscape [10,11].”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [10] R. Li, K. Zhang and J. Wang, Thermal dynamic phase transition of Reissner-Nordström Anti-de Sitter black holes on free energy landscape, JHEP 10 (2020) 090 [arXiv:2008.00495] [INSPIRE]. source
    • cites [11] R. Li, K. Zhang and J. Wang, Probing black hole microstructure with the kinetic turnover of phase transition, Phys. Rev. D 104 (2021) 084076 [arXiv:2102.09439] [INSPIRE]. source

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisecitation

    The small/large RNAdS black hole phase transition has similar behavior with the Van der Waals fluid.

    “The small/large Reissner-Nordstrom AdS (RNAdS) black hole phase transition, which is another type of first order phase transition and has the similar behavior with the Van der Walls fluid [9], was also extensively investigated by researchers.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [9] D. Kubiznak and R.B. Mann, P-V criticality of charged AdS black holes, JHEP 07 (2012) 033 [arXiv:1205.0559] [INSPIRE]. source

  • Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.

    Interpretationnone given

    The bubble nucleation process from the SAdS black hole to the AdS space is the analogy of the Hawking-Page phase transition.

    “The bubble nucleation process from the SAdS black hole to the AdS space is the analogy of the Hawking-Page phase transition.”
    Quote in the paperNot a substantial claim
    • The authors state this as an assumption: The bubble wall is uncharged.
    • The authors state this as an assumption: The energy-momentum tensor of the wall is S_ab = -σ h_ab, where σ is the tension of the wall.
    • The authors state this as an assumption: The vacuum energy of the interior spacetime is smaller than that of the exterior spacetime, i.e. L+ > L-.
    • The authors state this as an assumption: The bubble nucleation has O(3) symmetry.
    • The authors state this as an assumption: The bubble wall is thin.
7 of 7

  • The authors state this as an assumption.

    The bubble wall is uncharged.

    “In the present work, we consider the case that the thin shell is uncharged, and set G = 1 without loss of generality.”
    “At last, we should point our the thin wall model considered in the present work is uncharged.”

  • The authors state this as an assumption.

    The energy-momentum tensor of the wall is S_ab = -σ h_ab, where σ is the tension of the wall.

    “We assume S ab = -σh ab , where σ is the tension of the wall.”

  • The authors state this as an assumption.

    The vacuum energy of the interior spacetime is smaller than that of the exterior spacetime, i.e. L+ > L-.

    “We consider the case that the vacuum energy of the interior spacetime is smaller than that of the exterior spacetime, i.e.L + > L -.”

  • The authors state this as an assumption.

    The bubble nucleation has O(3) symmetry.

    “Considering the symmetry of the metrics, the bubble nucleation with O(3)-symmetry is described by the local coordinates on each side of the wall X a ± = {t ± (λ), r ± (λ), θ, φ} , (2.4)”

  • The authors state this as an assumption.

    The bubble wall is thin.

    “The bubble wall is taken to be thin for simplicity.”

  • The paper relies on this without support.

    The bubble nucleation process taking spatial inhomogeneity into account had not been investigated before this work.

    “However, the bubble nucleation process by taking the spatial inhomogeneous into account was not investigated until now.”

  • The authors state this as an assumption.

    The interior and exterior spacetimes separated by the bubble wall are two different AdS black holes with different cosmological constant or vacuum energy.

    “The interior and the exterior spacetimes separated by the bubble wall are two different AdS black holes with different cosmological constant or vacuum energy.”

  • The authors state this as an assumption.

    The electric charge of the spacetime is set to Q on both sides of the wall.

    “Therefore, we take Q + = Q -= Q.”
8 of 8

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Metadata

Authors
Li, R., & Wang, J.
Affiliations
Stony Brook University (US)
Corresponding author
Wang, Jin
ORCID
Venue
Journal of High Energy Physics
Publisher
Springer Science and Business Media LLC
Published
2022-09-19
Volume
2022
Issue
9
ISSN
1029-8479 (ISSN-L)
DOI
10.1007/jhep09(2022)151
OpenAlex
W4283453538
Semantic Scholar
0d367d14cddc619a7cba55fee6e6d41bc65a8f9a
Cited by
2
References
43
Citations by year
2025: 1 · 2024: 1
FWCI
0.06
Type
journal article
Language
en
Open access
Licence
Locations
  • Journal of High Energy Physics (publishedVersion, cc-by)
  • arXiv (Cornell University) (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
  • arXiv (Cornell University)
Topics
  • Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
  • Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Particle physics theoretical and experimental studies
Keywords
vacuum decay, bubble nucleation, AdS black holes, Euclidean action, tunneling rate, Reissner-Nordström-AdS black hole, cosmological constant, bubble walls

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