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Cited by 140Particle physics theoretical and experimental studiesBlack Holes and Theoretical PhysicsNoncommutative and Quantum Gravity Theories

The DOI matches its Crossref record; 24 of the 25 references it cites were found in a registry or an index, and 1 are not checked yet; none of the 21 sources its claims cite is checked for support yet.

Gravity and the Stability of the Higgs Vacuum

Open access
Burda, Philipp, Gregory, Ruth, Moss, Ian G.·2015·Physical Review Letters
DOI 10.1103/physrevlett.115.071303
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Abstract

We discuss the effect of gravitational interactions on the lifetime of the Higgs vacuum where generic quantum gravity corrections are taken into account. Using a "thin-wall" approximation, we provide a proof of principle that small black holes can act as seeds for vacuum decay, spontaneously nucleating a new Higgs phase centered on the black hole with a lifetime measured in millions of Planck times rather than billions of years. The corresponding parameter space constraints are, however, extremely stringent; therefore, we also present numerical evidence suggesting that with thick walls, the parameter space may open up. Implications for collider black holes are discussed.

Checked 2026-11-09 · 1 reference not checked yet

Overview

AI snapshot

Written from the paper’s full text.

TL;DR

Gravitational impurities in the form of small black holes can seed Higgs vacuum decay, with thin-wall calculations showing bounce actions suppressed from about \(10^6\) to \(10^{0-2}\) and thick-wall numerics indicating primordial black holes may trigger catastrophic vacuum decay. The effect is highly parameter-dependent, and collider black holes are less risky because extra dimensions suppress the branching ratio.

Key findings

  • In the thin-wall Coleman–de Luccia extension with a black hole, small black holes can act as seeds for vacuum decay, nucleating a new Higgs phase centered on the black hole with a lifetime measured in millions of Planck times rather than billions of years. As the seed black hole mass increases, the instanton action drops rapidly; at a critical mass \(M_C\), a static bubble wall exists, and unless \(\sigma \ell\) is Planck scale, the suppression is several orders of magnitude, changing the exponential factor from an irrelevant \(10^6\) to a potentially relevant \(10^{0-2}\).
  • The branching ratio of tunneling to Hawking evaporation is \(\Gamma_D/\Gamma_H \approx 44(M_+^2/M_p^2)B^{1/2}e^{-B}\). For thin-wall instantons, there is a range of \(M_+\) (small, though still above the Planck mass) with strong enhancement, and tunneling dominates.
  • The thin-wall condition is very constraining: the allowed range of \(\lambda_6\) is small and occurs for large values \(\lambda_6 \sim 10^3\)–\(10^5\), depending on \(\lambda_*\).
  • Thick-wall numerical solutions with \(\lambda_*=-0.01\) and \(b=10^{-4}\) show that primordial black holes evaporating into the relevant mass range make vacuum decay more probable; for a \(10^5 M_p\) mass black hole the evaporation timescale is \(\sim 10^{-28}\) s, so any primordial black holes will eventually trigger a catastrophic phase transition, ruling out potentials with parameters in those ranges. Collider black holes are less risky because extra dimensions tend to suppress the branching ratio.

Methods

  • The authors extend the Coleman–de Luccia thin-wall method to include a black hole, deriving a bounce action for a wall bounding two spacetime regions with different cosmological constants and black hole masses, then estimating the decay rate and branching ratio.
  • They perform a preliminary numerical investigation of static instantons by solving the Einstein-scalar equations with rotational symmetry on a black hole AdS background, using a spherically symmetric metric ansatz and a shooting technique that varies the scalar field at the black hole horizon and aims for \(\varphi \to 0\) as \(r \to 0\), with representative Higgs parameters \(\lambda_*=-0.01\) and \(b=10^{-4}\).
  • For collider black holes, they estimate the effect by modelling the instanton with a higher-dimensional counterpart, replacing \(R \to R^{n+1}\), with horizon areas \(A \propto M^{(n+2)/(n+1)}\) and evaporation temperature \(T \propto M^{-1/(n+1)}\).

Limitations

  • Stated: the thin-wall approximation is very constraining; the pseudo-analytic discussion is limited in parameter space; a full exploration outside the thin-wall approximation is necessary; the numerical investigation is preliminary; the collider black hole process is beyond the analytic approximations used; the conclusion depends on the existence of small black holes and a detailed numerical study of parameter space; and the semiclassical bubble nucleation argument only applies when the action \(B>1\).
  • Stated: the discussion assumes no impact from new physics between the TeV scale and the Planck scale, although generic quantum gravity corrections are included.
  • Evident: the results rely on representative parameter choices and on thin-wall, static-instanton, and higher-dimensional modelling approximations, without a full parameter scan or exact higher-dimensional black hole solutions.

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

Integrity signals

Registry

Crossref · 10.1103/physrevlett.115.071303

Cites

24 of 25 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Verification

Claims the paper makes

0 of 21 cited sources checked · 0 supported · 0 flagged

  • Findingreasoning

    Computing the branching ratio for these thin-wall models shows that tunneling does indeed dominate.

    “On the other hand, computing the branching ratio, (7), for these models shows that tunneling does indeed dominate.”
    Quote in the paperSubstantial claim
  • Findingown data

    For thin wall instantons, there is a range of M+ (small, though still above Planck mass) for which there is very strong enhancement of bubble tunneling.

    “For our thin wall instantons, there is indeed a range of M + (small, though still above the Planck mass), for which we have very strong enhancement of bubble tunneling.”
    Quote in the paperSubstantial claim
  • Findingnone given

    The parameter space constraints for the thin-wall black-hole-seeded vacuum decay are extremely stringent.

    “The corresponding parameter space constraints are extremely stringent however, therefore we also present numerical evidence suggesting that with thick walls, the parameter space may open up.”
    Quote in the paperSubstantial claim
  • Findingown data

    Numerical evidence suggests that with thick walls, the parameter space for black-hole-seeded vacuum decay may open up.

    “The corresponding parameter space constraints are extremely stringent however, therefore we also present numerical evidence suggesting that with thick walls, the parameter space may open up.”
    Quote in the paperSubstantial claim
  • Findingreasoning

    The effect of a black hole on the tunneling action can be very significant for low tension bubble walls and small mass black holes.

    “However, the effect of a black hole, (5), on the tunneling action can be very significant for low tension bubble walls and small mass black holes.”
    Quote in the paperSubstantial claim
  • It may state two separate claims as one. 17
  • Probably not a substantial claim. 5

  • It may state two separate claims as one.

    Findingreasoning

    As seed black hole mass increases further, the nucleated bubble has a black hole remnant in its interior, and the action rises with increasing seed mass.

    “As the seed black hole mass increases further, the nucleated bubble now has a black hole remnant in the bubble interior, with the action now rising with increasing seed mass.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Findingreasoning

    Using a thin-wall approximation, small black holes can act as seeds for vacuum decay, spontaneously nucleating a new Higgs phase centered on the black hole with a lifetime measured in millions of Planck times rather than billions of years.

    “Using a”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Findingown data

    Scanning parameter space shows requiring a thin wall is very constraining: the range of λ_6 for which this occurs is very small, and occurs for large values of λ_6 ∼ 10^3-10^5, depending on λ_*.

    “scanning through parameter space we find that requiring a thin wall is very constraining: the range of λ 6 for which this occurs is very small, and occurs for large values of the parameter λ 6 10 3 -10 5 , depending on λ * .”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Findingreasoning

    Unless σl is Planck scale, the suppression of the bounce action at M_C is several orders of magnitude, changing the exponential factor from 10^6 to 10^{0-2}.

    “unless the combination σℓ is Planck scale, this suppression is several orders of magnitude at M C , thus changing the exponential factor in (6) from an irrelevant 10 6 to a potentially extremely relevant 10 0-2 .”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Findingreasoning

    The calculation is relatively insensitive to the number of extra dimensions (horizon areas A ∝ M^{(n+2)/(n+1)}), whereas the evaporation rate of black holes is enhanced due to increased Hawking temperature T ∝ M^{-1/(n+1)} and grey-body factors.

    “It turns out this calculation is relatively insensitive to the number of extra dimensions (the horizon areas A ∝ M (n+2)/(n+1) ) whereas the evaporation rate of black holes is enhanced, in part because of the increased Hawking temperature, T ∝ M -1/(n+1) , and in part because of grey-body factors.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Findingreasoning

    As the seed black hole mass M+ is switched on, the instanton action drops rapidly, and the bubble initially nucleates by removing the black hole.

    “As the seed black hole mass M + is switched on, the instanton action drops rapidly, and the bubble initially nucleates by removing the black hole.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Findingreasoning

    At M_C, an unstable static bubble nucleates which will either recollapse or expand with roughly equal probability.

    “In this case, an unstable static bubble nucleates which will either recollapse or expand with roughly equal probability.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Findingreasoning

    As the seed black hole mass increases, a critical mass M_C is reached at which the potential V(R) has a single point with V=V'=0, and a static bubble wall solution exists.

    “However, as the seed black hole mass continues to increase, a critical mass M C is reached at which the potential V (R) has a single point at which V = V = 0, and there exists a static bubble wall solution.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Interpretationreasoning

    Gravitational interactions can affect the lifetime of the Higgs vacuum, but only if small black holes nucleate the decay.

    “We will show that it can, although only if small black holes nucleate the decay.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Premisecitation

    Typically the CDL action is O(10^{3-6}) for Higgs potentials, leading to huge exponential suppression and the conclusion that gravitational tunneling is irrelevant.

    “Typically, the CDL action is of order O(10 3-6 ) for the Higgs potentials, leading to a huge exponential suppression of the decay rate, and to the conclusion that gravitational tunneling is irrelevant.”
    Quote in the paperSubstantial claim0 of 3 sources checked
    • cites [3]

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • cites [4]

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • cites [5]

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • It may state two separate claims as one.

    Interpretationcitation

    With currently measured Higgs and top quark masses, λ_eff near the Planck scale is small with a preference towards negative values.

    “with the currently measured values it seems that λ eff near the Planck scale is small with a preference towards negative values.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [13]

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

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

    Premisenone given

    The semi-classical bubble nucleation argument only applies when the action B > 1.

    “Note that the semi-classical bubble nucleation argument only applies when the action B > 1.”
    Quote in the paperNot a substantial claim

  • It may state two separate claims as one.

    Premisecitation

    The running of the Higgs coupling quite possibly makes our vacuum only metastable, with the true Higgs vacuum at large expectation values and negative vacuum energy.

    “the running of the coupling of the Higgs quite possibly means that our vacuum is only metastable, and the true Higgs vacuum in fact lies at large expectation values of the Higgs and negative vacuum energy.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [13]

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • The authors state this as an assumption: There is no impact from new physics between the TeV scale and the Planck scale.

  • It may state two separate claims as one.

    Interpretationreasoning

    The branching ratio tends to be suppressed with extra dimensions, making collider black holes less risky for vacuum decay, however black holes produced by particle collisions could still cause vacuum decay in certain regions of parameter space.

    “The branching ratio tends to be suppressed with extra dimensions, making collider black holes less risky for vacuum decay, however black holes produced by particle collisions could still cause vacuum decay in certain regions of parameter space.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim. The paper may give no reason why it holds.

    Premisenone given

    The thin wall approximation requires the energy at the potential minimum to be smaller than the potential barrier height.

    “The main wrinkle in this argument is that the condition for the thin wall approximation requires that the energy at the potential minimum is smaller than the potential barrier height”
    Quote in the paperNot a substantial claim

  • It may state two separate claims as one.

    Interpretationreasoning

    With these Higgs potentials, the presence of any primordial black holes will eventually trigger a catastrophic phase transition from our standard model vacuum, thus ruling out potentials with parameters in these ranges.

    “Hence with these Higgs potentials, the presence of any primordial black holes will eventually trigger a catastrophic phase transition from our standard model vacuum thus ruling out potentials with parameters in these ranges.”
    Quote in the paperSubstantial claim

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

    Premisecitation

    Evaporation rates for higher-dimensional black holes have been computed assuming a higher dimensional Myers-Perry solution, with emission cross sections appropriate to a braneworld scenario.

    “evaporation rates have been computed assuming a higher dimensional Myers-Perry solution [18], with emission cross sections appropriate to a braneworld scenario [19].”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [18]

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • cites [19]

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • It may state two separate claims as one.

    Premisenone given

    Although black holes produced in the early universe start with relatively high masses, their temperature is above that of the microwave background, and they evaporate down into the range plotted in figure 3.

    “Although black holes produced in the early universe start out with relatively high masses, their temperature is nonetheless above that of the microwave background, and they evaporate down into the range plotted in figure 3.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Interpretationreasoning

    The addition of a seed black hole changes the energy balance so that bubbles form at a smaller radius, lowering the instanton action and enhancing decay.

    “the bubble forms around the (euclidean) black hole but because of the distortion of space the payoff between volume inside a bubble and its surface area is changed, and bubbles form at a smaller radius and hence the 'cost' of forming them is lower: the instanton has a smaller action and the decay process can be significantly enhanced.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Premisecitation

    The fit to [13] gives parameter ranges -0.01 ≤ λ_* ≤ 0, 0.1 M_p ≤ φ_* ≤ M_p, and b ∼ 10^-4.

    “where the fit to the results of [13] give parameter ranges -0.01 λ * 0, 0.1M p φ * M p and b ∼ 10 -4 .”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [13]

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Probably not a substantial claim.

    Study design and conductnone given

    This range is well above the Planck mass, where the paper has some confidence in the validity of the vacuum decay calculation.

    “Note that this range is well above the Planck mass, where we have some confidence in the validity of the vacuum decay calculation.”
    Quote in the paperSubstantial claim

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

    Premisecitation

    In Ref. [6], it was shown that the action is given by the area terms in (5), as in the thin wall case.

    “In Ref. [6], it was shown that the action is given by the area terms in (5), as in the thin wall case.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [6]

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

22 of 22

  • The authors state this as an assumption.

    The standard model false vacuum has zero cosmological constant (Λ+ = 0).

    “For the decay of the Higgs vacuum, we assume the standard model has Λ + = 0”

  • The authors state this as an assumption.

    There is no impact from new physics between the TeV scale and the Planck scale.

    “Of course this discussion assumes no impact from new physics between the TeV scale and the Planck scale.”

  • The authors state this as an assumption.

    The higher-dimensional collider black hole instanton can be modelled with a static bubble.

    “Assuming the static bubble we can then calculate the horizon radius and area”

  • The paper relies on this without support.

    Small black holes exist (e.g., primordial or produced at colliders) so that they can seed vacuum decay.

    “Such a conclusion of course depends on the existence of said small black holes -by no means a certainty -and a detailed numerical study of parameter space.”
4 of 4

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • In [29,30], the tunnelling exponent did not depend on the periodicity of the Euclidean time (temperature).

    “In [29,30], we found that the tunnelling exponent did not depend on the periodicity of the Euclidean time, in other words, on the value of the temperature.”

    From The fate of the Higgs vacuum (2016) · cites this paper as [29]

    Our copy says that for static instantons the action is given by the black-hole horizon-area terms in Eq. (5), and that the calculation treats conical deficits when periodicities differ. This supports independence from Euclidean-time periodicity for the static solutions studied, but the paper also gives a more general instanton action with an additional integral; it does not establish the claim for tunnelling exponents without that qualification. The supplied passages have no page labels. (LLM, conf=0.82)

    Experimental — accuracy not yet measured

  • For each seed mass black hole, there exists a unique least action instanton with a unique remnant black hole mass.

    “These Euclidean solutions exist in principle with all possible values of interior and exterior mass terms, however, for each seed (exterior) mass black hole, there exists a unique least action instanton with a unique remnant (interior) black hole mass.”

    From The fate of the Higgs vacuum (2016) · cites this paper as [29]

    The passage on the critical seed mass (section labeled Abstract; page unavailable) describes a static bubble solution and says that bubbles formed at higher seed masses leave an interior black-hole remnant. It does not establish a unique least-action instanton or a unique remnant mass for each seed mass; at lower seed masses, it says the bubble initially removes the black hole. (LLM, conf=0.83)

    Experimental — accuracy not yet measured

  • For very small seed masses, there are instanton solutions that remove the black hole, and the solution has the form of a perturbed CDL instanton.

    “For very small seed masses, there are instanton solutions that remove the black hole, and the solution has the form of a perturbed CDL instanton.”

    From The fate of the Higgs vacuum (2016) · cites this paper as [29]

    The passage labeled “Abstract” says that when the seed black-hole mass is first switched on, the bubble nucleates by removing the black hole. It also describes extending the Coleman–de Luccia thin-wall method to include a black hole, but does not establish that the resulting solution has the form of a perturbed CDL instanton. (LLM, conf=0.83)

    Experimental — accuracy not yet measured

  • In [29], preliminary evidence was provided that the parameter space restriction was an artefact of the constraints imposed on the potential by demanding a thin-wall approximation.

    “In [29], we provided preliminary evidence that this parameter space restriction was an artefact of the constraints imposed on the potential by demanding that it allow a thin-wall approximation for the instanton.”

    From The fate of the Higgs vacuum (2016) · cites this paper as [29]

  • In [29,30], the authors provided a proof of principle that the lifetime of the vacuum could become precipitously short in the presence of primordial black holes.

    “Applying these ideas to the Higgs vacuum, in [29,30] we recently provided a proof of principle that the lifetime of the vacuum could become precipitously short in the presence of primordial black holes, paralleling the intuition of impurities catalysing a phase transition.”

    From The fate of the Higgs vacuum (2016) · cites this paper as [29]

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Metadata

Authors
Burda, P., Gregory, R., & Moss, I. G.
Affiliations
  • Durham University (GB)
  • Perimeter Institute (CA)
  • Newcastle University (GB)
ORCID
Venue
Physical Review Letters
Publisher
American Physical Society (APS)
Published
2015-08-13
Volume
115
Issue
7
Pages
071303-071303
ISSN
  • 0031-9007 (ISSN-L)
  • 1079-7114
DOI
10.1103/physrevlett.115.071303
OpenAlex
W1575417833
Semantic Scholar
80c127bf76dd784c1f98d00e04ecdc15dd0d3551
Cited by
140
References
20
Citations by year
2026: 8 · 2025: 16 · 2024: 12 · 2023: 9 · 2022: 13 · 2021: 13 · 2020: 15 · 2019: 11 · 2018: 14 · 2017: 10 · 2016: 11 · 2015: 8
FWCI
6.86
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical Review Letters (publishedVersion)
  • PubMed (publishedVersion)
  • arXiv (Cornell University) (acceptedVersion)
  • Durham Research Online (Durham University) (acceptedVersion)
  • Durham Research Online (Durham University) (submittedVersion, cc-by)
  • arXiv (Cornell University)
  • Newcastle University ePrints (Newcastle Univesity) (cc-by-nc)
Funders
  • Engineering and Physical Sciences Research Council
  • Science and Technology Facilities Council (ST/L000407/1)
  • Wolfson Foundation
  • Ministry of Research and Innovation
Topics
  • Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Particle physics theoretical and experimental studies
  • Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
  • Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Noncommutative and Quantum Gravity Theories
Keywords
Higgs vacuum stability, vacuum decay, gravitational corrections, quantum gravity, thin-wall approximation, black holes, spontaneous nucleation, Higgs phase, parameter space constraints

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