The DOI matches its Crossref record; 30 of the 30 references it cites were found in a registry or an index; none of the 21 sources its claims cite is checked for support yet.
Gravity and the Stability of the Higgs Vacuum
Open accessAbstract
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.
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
Cites
Statistics
Verification
Claims the paper makes
16 Sources not found · 15 No basis given · 9 Own interpretation · 4 Own result · 1 Own method
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“On the other hand, computing the branching ratio, (7), for these models shows that tunneling does indeed dominate.”
§ Gravity and the stability of the Higgs vacuum > Abstract
boosteddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“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.”
§ Gravity and the stability of the Higgs vacuum > Abstract
boosteddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“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.”
§ Gravity and the stability of the Higgs vacuum > Abstract
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“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.”
§ Gravity and the stability of the Higgs vacuum > Abstract
hedgedconditional- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“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.”
§ Gravity and the stability of the Higgs vacuum > Abstract
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“This provides a 'proof of principle' and motivates a numerical analysis of Higgs instantons, which confirm the presence of strongly enhanced decay in the presence of black holes.”
§ Gravity and the stability of the Higgs vacuum > Abstract
boosteddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“At this point, the mass hits a range in which vacuum decay is more probable, i.e. the tunneling half life becomes smaller than the (instantaneous) Hawking lifetime of the black hole.”
§ Gravity and the stability of the Higgs vacuum > Abstract
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
In the paper
“Recently in [6] we investigated the impact of gravitational impurities, in the guise of black holes, on the usual Coleman de Luccia picture (see also [7,8] for early investigations of this issue) and found a significant enhancement of vacuum decay in a wide range of cases”
§ Gravity and the stability of the Higgs vacuum > Abstract
What the sources say
- Not matchedcites [6]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- Not matched
In the paper
“the action of a general instanton with a black hole was found to be B = A + h 4G - A - h 4G (5 ) + 1 4G dλ {(2R -6GM + ) τ+ -(2R -6GM -) τ-}”
§ Gravity and the stability of the Higgs vacuum > Abstract
What the sources say
- Not matchedcites [6]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- Not matched
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Given that this evaporation timescale is ∼ 10 -28 s for a 10 5 M p mass black hole, it is clear that once a primordial black hole nears the end of its life cycle, it will seed vacuum decay in these models.”
§ Gravity and the stability of the Higgs vacuum > Abstract
boosteddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- It may state two separate claims as one. 17
- Probably not a substantial claim. 5
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“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.”
§ Gravity and the stability of the Higgs vacuum > Abstract
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Using a”
§ Gravity and the stability of the Higgs vacuum > Abstract
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“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 * .”
§ Gravity and the stability of the Higgs vacuum > Abstract
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“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 .”
§ Gravity and the stability of the Higgs vacuum > Abstract
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“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.”
§ Gravity and the stability of the Higgs vacuum > Abstract
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“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.”
§ Gravity and the stability of the Higgs vacuum > Abstract
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“In this case, an unstable static bubble nucleates which will either recollapse or expand with roughly equal probability.”
§ Gravity and the stability of the Higgs vacuum > Abstract
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“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.”
§ Gravity and the stability of the Higgs vacuum > Abstract
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We will show that it can, although only if small black holes nucleate the decay.”
§ Gravity and the stability of the Higgs vacuum > Abstract
plainconditional- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
None of the sources cited for this claim could be matched to a paper in Crossref, so there is nothing to check it against.
In the paper
“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.”
§ Gravity and the stability of the Higgs vacuum > Abstract
What the sources say
- Not matchedcites [3]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Not matchedcites [4]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Not matchedcites [5]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- Not matched
In the paper
“with the currently measured values it seems that λ eff near the Planck scale is small with a preference towards negative values.”
§ Gravity and the stability of the Higgs vacuum > Abstract
What the sources say
- Not matchedcites [13]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
hedgedcorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- Not matched
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Note that the semi-classical bubble nucleation argument only applies when the action B > 1.”
§ Gravity and the stability of the Higgs vacuum > Abstract
plainconditional- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
In the paper
“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.”
§ Gravity and the stability of the Higgs vacuum > Abstract
What the sources say
- Not matchedcites [13]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
hedgedconditional- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- The authors state this as an assumption: There is no impact from new physics between the TeV scale and the Planck scale.
- Not matched
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“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.”
§ Gravity and the stability of the Higgs vacuum > Abstract
hedgeddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“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”
§ Gravity and the stability of the Higgs vacuum > Abstract
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper may give no reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“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.”
§ Gravity and the stability of the Higgs vacuum > Abstract
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
None of the sources cited for this claim could be matched to a paper in Crossref, so there is nothing to check it against.
In the paper
“evaporation rates have been computed assuming a higher dimensional Myers-Perry solution [18], with emission cross sections appropriate to a braneworld scenario [19].”
§ Gravity and the stability of the Higgs vacuum > Abstract
What the sources say
- Not matchedcites [18]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Not matchedcites [19]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
- Not matched
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“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.”
§ Gravity and the stability of the Higgs vacuum > Abstract
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“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.”
§ Gravity and the stability of the Higgs vacuum > Abstract
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
In the paper
“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 .”
§ Gravity and the stability of the Higgs vacuum > Abstract
What the sources say
- Not matchedcites [13]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- Not matched
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“Note that this range is well above the Planck mass, where we have some confidence in the validity of the vacuum decay calculation.”
§ Gravity and the stability of the Higgs vacuum > Abstract
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
In the paper
“In Ref. [6], it was shown that the action is given by the area terms in (5), as in the thin wall case.”
§ Gravity and the stability of the Higgs vacuum > Abstract
What the sources say
- Not matchedcites [6]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
- Not matched
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.”
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?
The source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“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]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“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]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“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]
Experimental — accuracy not yet measuredThe cited source says what the claim attributes to it.
In the citing paper
“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]
The cited source says what the claim attributes to it.
In the citing paper
“The possibility of vacuum decay caused by black holes formed from collisions was considered JHEP06(2016)025 in [29,30].”
From The fate of the Higgs vacuum (2016) · cites this paper as [29]
In the citing paper
“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]
In the citing paper
“For larger black hole seeds (beyond a critical mass M C depending on the vacuum energy and the surface tension of the wall) the remnant mass is non-zero and the minimum action solution becomes static in the complex time coordinate.”
From The fate of the Higgs vacuum (2016) · cites this paper as [29]
Citations
Cites
Large Mass Hierarchy from a Small Extra Dimension
Randall, L., & Sundrum, R. (1999) · Physical Review Letters · doi:10.1103/physrevlett.83.3370 · Cited by 9,227
The hierarchy problem and new dimensions at a millimeter
Arkani–Hamed, N., Dimopoulos, S., & Dvali, G. (1998) · Physics Letters B · doi:10.1016/s0370-2693(98)00466-3 · Cited by 6,563
Fate of the false vacuum: Semiclassical theory
Coleman, S. (1977) · Physical Review D · doi:10.1103/physrevd.15.2929 · Cited by 2,552
Black holes in higher dimensional space-times
Myers, R. C., & Perry, M. J. (1986) · Annals of Physics · doi:10.1016/0003-4916(86)90186-7 · Cited by 2,125
Black Holes in the Early Universe
Carr, B. J., & Hawking, S. W. (1974) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/168.2.399 · Cited by 1,827
Fate of the false vacuum. II. First quantum corrections
Callan, C. G., & Coleman, S. (1977) · Physical Review D · doi:10.1103/physrevd.16.1762 · Cited by 1,789
Gravitational effects on and of vacuum decay
Coleman, S., & De Luccia, F. (1980) · Physical Review D · doi:10.1103/physrevd.21.3305 · Cited by 1,537
Higgs mass and vacuum stability in the Standard Model at NNLO
Degrassi, G., Di Vita, S., Elias-Miró, J., Espinosa, J. R., Giudice, G. F., Isidori, G., & Strumia, A. (2012) · Journal of High Energy Physics · doi:10.1007/jhep08(2012)098 · Cited by 1,524
Particle emission rates from a black hole: Massless particles from an uncharged, nonrotating hole
Page, D. N. (1976) · Physical Review D · doi:10.1103/physrevd.13.198 · Cited by 1,133
Black Holes at the Large Hadron Collider
Dimopoulos, S., & Landsberg, G. (2001) · Physical Review Letters · doi:10.1103/physrevlett.87.161602 · Cited by 1,081
Cited by
Sorted by citations
Constraints on primordial black holes
Carr, B., Kohri, K., Sendouda, Y., & Yokoyama, J. (2021) · Reports on Progress in Physics · doi:10.1088/1361-6633/ac1e31 · Cited by 1,156
Cosmological phase transitions: From perturbative particle physics to gravitational waves
Athron, P., Balázs, C., Fowlie, A., Morris, L., & Wu, L. (2023) · Progress in Particle and Nuclear Physics · doi:10.1016/j.ppnp.2023.104094 · Cited by 323
The cosmological Higgstory of the vacuum instability
Espinosa, J. R., Giudice, G. F., Morgante, E., Riotto, A., Senatore, L., Strumia, A., & Tetradis, N. (2015) · Journal of High Energy Physics · doi:10.1007/jhep09(2015)174 · Cited by 247
Gravitational wave production right after a primordial black hole evaporation
Inomata, K., Kawasaki, M., Mukaida, K., Terada, T., & Yanagida, T. T. (2020) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.101.123533 · Cited by 194
Cosmological Aspects of Higgs Vacuum Metastability
Markkanen, T., Rajantie, A. K., & Stopyra, S. (2018) · Frontiers in Astronomy and Space Sciences · doi:10.3389/fspas.2018.00040 · Cited by 146
Metadata
- Authors
- Burda, P., Gregory, R., & Moss, I. G.
- Affiliations
- Durham University (GB)
- Perimeter Institute (CA)
- Newcastle University (GB)
- 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
- 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
- bronze
- doi.org
- 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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
A language model drew the claims from the paper on 2026-11-09, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).
A second model labelled each claim on 2026-11-09 (model jev-1.13-20260917, definition revision gold-guideline-v0.2).
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
