Light Black Holes from Light

Don N. Page

REVIEW 3 major objections 4 minor 1 cited by

Light Black Holes from Light

T0 review · 3 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Two colliding light pulses can form a black hole near the Planck mass before pair production halts the collapse.

desk verdict A clean, honest counterexample to 'No Black Holes from Light' that is plausibly right; the pair-production bound is assumed rather than derived, but the exponential suppression outside the horizon makes the conclusion robust to most plausible corrections. read the letter →

arxiv 2505.16202 v1 pith:JBJNRSBB submitted 2025-05-22 hep-th gr-qc

Don N. Page This is my paper · ORCID

classification hep-thgr-qc

keywords kugelblitzeblackholeformationfromlightSchwingerpairproductionplane-wavepulsecollisionhoopconjecturePlanckmassquantumelectrodynamicseventhorizon

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper takes on the recent claim that black holes cannot be made from light because electron-positron pairs produced by vacuum polarization dissipate the energy before collapse. The author argues that the claim is not universal: in idealized initial states made of two counter-propagating, antiparallel-polarized plane-wave pulses, the electromagnetic invariants are such that the standard locally constant field approximation predicts zero pair production, and any residual pair production is exponentially suppressed outside the collapsing region. If the argument is right, pure light can form black holes in principle with masses down to near the Planck mass and radii near the Planck length, about 43 orders of magnitude below the lower radius suggested by the earlier no-go result. The author agrees such formation is highly implausible in our actual universe, but insists the laws of physics allow it in idealized theoretical settings.

What carries the argument

The load-bearing object is the two-pulse configuration of Eqs. (3)-(6): two gaussian plane-wave pulses moving in opposite directions along the $z$-axis, with antiparallel linear polarization. The key identity is the combined-field invariant $E^2-B^2=-4E_0^2\exp[-(t^2+z^2)/L^2]$, which is negative everywhere, so the field is purely magnetic in a suitable boost frame and the locally constant field approximation gives zero pair production. The pair-production estimate is carried by the conservative upper bound $N_{\rm max}=q^2E_0^2\pi^{-3}\exp[-(t^2+z^2)/L^2]$, whose Gaussian factor $\exp(-F^2)$ with $F=R/L$ suppresses pair production outside the collapsing sphere. The collapse criterion is the hoop condition $2M/R>1$, applied to the energy inside a sphere of radius $R$.

What would settle it

Compute the actual QED pair-production probability in the field of Eqs. (3)-(6) without the locally constant field approximation, integrating over the exterior region $t^2+z^2>R^2$ for a nominal collapse with $F=R/L=24$ and $\epsilon=(E_0L)^2\approx0.047$; if the energy carried away by escaping pairs exceeds $\sim q^3E_0\,e^{-F^2}$ of the enclosed mass, the pulse dissipates before collapse and the central claim is falsified.

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Extended reading notes

Core claim

The paper's central claim is that idealized pure-photon states exist that collapse to a black hole before electron-positron pair production can dissipate the energy, for black-hole masses down to near the Planck mass. The construction is a pair of counter-propagating gaussian plane-wave pulses, polarized so that the electric fields oppose while the magnetic fields add. For this field, $E\cdot B=0$ and $E^2-B^2<0$ everywhere, so at each spacetime point there is a Lorentz frame with only a magnetic field, and the locally constant field approximation predicts zero pair production. The paper then bounds any residual pair production by replacing $E$ with $B$ in the Schwinger rate, obtaining $N_{\rm max}=q^2E_0^2\pi^{-3}\exp[-(t^2+z^2)/L^2]$, and shows that outside the collapsing region this bound integrates to a tiny energy fraction $\lesssim q^3E_0^{-1}e^{-R^2/L^2}$ when $R/L\gg1$. With the hoop conjecture as the collapse criterion, the minimum mass is approximately $M_0\sim L/(2\sqrt{\pi}\,\epsilon)$ for $\epsilon=E_0^2L^2\ll1$, so masses not many times the Planck mass are reachable.

Load-bearing premise

The argument holds only if the real rate of electron-positron pair production in these colliding pulses stays below the paper's estimated ceiling; that rate is not derived from quantum electrodynamics because the standard locally constant field approximation gives zero pairs for this configuration.

Editorial extensions

If this is right

Pure light can form black holes in principle with masses only a few times the Planck mass and radii near the Planck length, far below the $10^{-29}$ m floor suggested by the earlier no-go analysis.
The impossibility claim must be read as a statement about realistic random-direction photon gases, not about all photon states; two collimated antiparallel pulses are an explicit idealized counterexample.
In the collision, essentially all pair production happens after the energy is already inside a horizon, so the pairs cannot carry energy away; only a fraction bounded by roughly $q^3E_0^{-1}e^{-F^2}$ of the black-hole mass can escape.
For a two-photon collision with COM energy $M$ in Planck units, the black-hole formation cross section $\sim M^2$ dominates the Breit-Wheeler pair-production cross section $\sim 0.14/M^2$, so gravitational collapse beats pair production at super-Planckian energies.
The minimum black-hole mass for given pulse parameters is approximately $M_0\sim L/(2\sqrt{\pi}\,\epsilon)$ with $\epsilon=E_0^2L^2\ll1$, and it can be approached by cutting off the pulses transversely near $R\sim 2M_0$.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A full time-dependent QED calculation of pair production in this two-pulse field is the natural next test; the paper's own conservative bound is not a derivation, so the exact threshold could shift, though the exponential suppression mechanism would remain.
The antiparallel-plane-wave construction suggests a general recipe for evading pair-production dissipation: keep the overlapping field magnetically dominated (or otherwise invariant-suppressed) while the energy focuses rapidly; other pulse shapes could be checked by the same method.
If the argument is correct, the practical obstruction to kugelblitze is not quantum electrodynamics but the impossibility of preparing nearly plane-wave pulses with sharp transverse cutoffs in any foreseeable laboratory setting.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Don Page's note is worth serious attention. It gives an explicit two-pulse collision geometry — counter-propagating, antiparallel-polarized Gaussian plane waves — for which the Schwinger invariants vanish, so the locally constant field approximation predicts zero pair production. The energy integrals and the hoop-condition inversion are clean, and the paper is unusually honest about what is assumed. The construction is genuinely new relative to Refs. [1] and [5], and the claim that the no-kugelblitze conclusion is not universal is plausibly right.

The soft spots are easy to name. Equation (25), the 'conservative upper bound' on pair production, is not derived; Page simply takes the constant-field formula, replaces the electric invariant by B, and drops the exponential. That is an assumption about QED in a time-dependent field, not a theorem. The hoop conjecture is used as a collapse criterion, the analysis is flat-spacetime, and the transverse cutoff is deferred. The paper admits all of this.

Having said that, I think the stress-test concern, while valid as a logical gap, may be less damaging than it sounds. For the F=24 example, the fields outside the would-be horizon are suppressed by e^{-576}, an utterly tiny number. Any local pair-production rate that vanishes with the field strength — whether it scales as B^2 or with higher derivatives — will be overwhelmed by that exponential. What would actually threaten the argument is a nonlocal pair production mechanism that is large even where the local fields are small, such as photon-photon scattering between the separated pulses. That is not ruled out by Eq. (25), but it is also not obviously favored by any known calculation. So the central conclusion is plausible and likely robust, but it is not rigorously established.

The paper is a modest, well-scoped contribution: a counterexample that changes the conceptual landscape, with no practical implications. As a referee, I would send it to review. The referee should ask for either a derivation of the bound or, at minimum, an explicit robustness argument showing that the conclusion survives plausible variants of the pair-production rate. The hoop-conjecture reliance should be stated as a conjecture, which it is. I would not desk reject it; it deserves to be on the record.

Referee Report

3 major / 4 minor

Summary. The paper challenges the recent claim that kugelblitze cannot form from light alone. It constructs two counter-propagating, antiparallel-polarized Gaussian pulses, computes the energy density and the hoop-conjecture condition for collapse, and then bounds pair production in the region outside the would-be black hole. The author concludes that black holes with mass not much larger than the Planck mass can form from light before pairs can dissipate the energy. The paper explicitly acknowledges that the hoop condition is used in flat spacetime, that the transverse cutoff of the pulses is not worked out, and that the pair-production estimate in Eq. (25) is taken as a conservative upper limit rather than derived from quantum electrodynamics.

Significance. If the central claim were established, it would provide an explicit in-principle counterexample to the 'No Black Holes from Light' theorem and would show that Planck-scale kugelblitze are not excluded by Schwinger dissipation alone. The paper contains clean analytic energy integrals, a transparent hoop-condition calculation, and the observation that the locally constant field approximation gives zero pair production for the constructed field. Those are useful contributions to the debate. However, the conclusion is currently conditional on an unproven pair-production bound, so the advertised counterexample is not yet established.

major comments (3)

[Sec. 3, Eq. (25)] Equation (25) is asserted as a 'conservative upper limit' by taking the constant-field formula (24), dropping the exponential, and replacing the invariant E with the invariant B. For the field (5)-(6) the invariant E vanishes, so the LCFA gives N=0; the replacement is not a QED bound. Since Eqs. (30)-(32) and the central conclusion that escaping pair energy is negligible follow from Eq. (25), the counterexample is not established unless a genuine upper bound or a real QED calculation is supplied.
[Sec. 3, Eq. (31)] The bound on the energy per pair, qE0R, is asserted without derivation. Because the paper itself argues that derivative effects are responsible for pair production in a field where LCFA gives zero, the particle spectrum cannot be assumed to be bounded by a static-field estimate. Without control on the energy distribution of produced pairs, the ratio E/M in Eq. (32) is not rigorously bounded.
[Secs. 2 and 3, transverse cutoff] The construction requires a transverse cutoff near r~R, but the details are declared beyond the scope of the paper. A cutoff introduces boundary fields and gradients that are themselves possible sources of pair production and also modify the hoop-condition integral. The statement that 'there should be no problem' needs at least a consistency argument or an explicit model of the cutoff.

minor comments (4)

[Sec. 2, Eq. (35)] The displayed inequality appears to be inverted: from Eq. (34) and R < 2M the condition is F > 2/(sqrt(pi) epsilon), not F > 2 sqrt(pi) epsilon. The text following Eq. (36) confirms the intended reciprocal form.
[Sec. 3, after Eq. (37)] The claim that L can be arbitrarily small is in tension with the requirement, stated in the same paragraph, that ML ≫ 1 for the classical approximation to be valid; for L -> 0 with fixed F, the number of photons becomes small.
[Sec. 4] The phrase 'even though such a scenario is very unlikely to occur in our present universe' is a useful caveat, but the conclusion should also explicitly state the dependence on the hoop conjecture, since the collapse criterion is not derived from general relativity.
[Sec. 5 and References] There is a typo in 'Engineeing' in the Acknowledgments, and Reference [14] repeats its title; please clean these up.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the construction is an explicit existence argument conditional on a stated pair-production upper bound, not a fit or self-citation chain.

full rationale

The paper's central derivation is self-contained: it constructs explicit Gaussian pulses, computes their energy density and applies the hoop-conjecture criterion 2M/R (Eqs. 12-21), then bounds escaping pair production using a deliberately adopted conservative upper limit (Eq. 25). That bound is admittedly not a QED derivation: the paper says, "I shall take as a conservative upper limit what one would get from Eq. (24) if one took the maximum value of 1 for the exponential and in the prefactor replaced the invariant E with the invariant B from Eq. (8), giving an upper limit for the pair-production rate per 4-volume of Nmax = ...". This is an unproven assumption, not a circular reduction: the paper does not fit the bound to match the conclusion, and the conclusion is not contained in the definition of the pulses. The hoop criterion is an external, standard condition; no parameter is fitted to a target outcome; and there are no load-bearing self-citations (the author cites standard QED results [9-14] and Thorne [15], not his own prior work). The acknowledged limitations, such as the uncertainty about pair energies and the unspecified transverse cutoff, bear on physical correctness and completeness, not on circularity. Under the stated assumptions the algebra from Eq. (25) through Eq. (32) is direct, so the derivation chain is not equivalent to its inputs by construction.

Assumptions & free parameters 2 free parameters · 3 assumptions · 0 invented entities

The central claim rests on the hoop conjecture, a flat-spacetime treatment, and an asserted bound on pair production that replaces the zero LCFA result. E0 and L are free choices of the initial state; no new particles or forces are introduced.

free parameters (2)

E0 = not fitted; example E0 L ≈ 0.217 for F=24
Maximum field amplitude of each Gaussian pulse; chosen by hand to satisfy the hoop condition while keeping the invariant fields small.
L = as small as Planck length in principle
Characteristic pulse length along the propagation direction; the paper argues no reason prevents L near the Planck length.

assumptions (3)

domain assumption Hoop conjecture: a black hole forms when 2M/R ≥ 1 for energy within a sphere of radius R in flat spacetime.
Used in Section 2 (Eq. 12 and surrounding text) as the sufficient condition for collapse; standard but unproven in classical gravity.
ad hoc to paper The pair-production rate is bounded by Nmax = q^2 E0^2 / pi^3 exp[-(t^2+z^2)/L^2].
Introduced in Section 3, Eq. (25); not derived from QED. The LCFA gives zero for the constructed field, so the actual rate is unknown and this bound is a modeling choice.
domain assumption Flat-spacetime approximation for energy integrals and hoop condition, neglecting curvature and gravitational focusing.
Acknowledged in Section 2 before Eq. (29); the author notes focusing would likely make formation easier, but the estimate is order-of-magnitude.

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Cite this review

Pith. "Pith review of Light Black Holes from Light." pith.science (2026). https://pith.science/paper/JBJNRSBB

@misc{pith2026250516202,
  author       = {Pith},
  title        = {Pith review of: Light Black Holes from Light},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JBJNRSBB}},
  note         = {Machine review of arXiv:2505.16202}
}

abstract

Alvarez-Dominguez, Garay, Martin-Martinez, and Polo-Gomez have suggested that ``it is not possible to concentrate enough light to precipitate the formation of an event horizon. We argue that the dissipative quantum effects coming from the self-interaction of light (such as vacuum polarization) are enough to prevent any meaningful buildup of energy that could create a black hole in any realistic scenario,'' and ``the dissipation of energy via Schwinger effect alone is enough to prevent the formation of kugelblitze with radii ranging from $10^{-29}$ to $10^8$ m.'' While I agree that it is indeed highly implausible that black holes will form mainly from light in our actual universe, either naturally or by any foreseeable human activity, there are many idealized theoretical processes for forming black holes of any size down to near the Planck length (about $10^{-35}$ m) purely from photons, such as from colliding approximately plane-wave pulses, with only a small fraction of the energy escaping the black hole as scattered light or electron-positron pairs.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

The weight of light: colliding pulses of radiation in General Relativity
gr-qc 2026-07 conditional novelty 6.0 of 10

Focused pulses of electromagnetic radiation can self-gravitate into black holes and, just below the collapse threshold, into ultracompact horizonless states whose measured compactness exceeds the hoop-conjecture value.

Reference graph

Works this paper leans on

14 extracted references · 9 canonical work pages · cited by 1 Pith paper

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D. Blas, V. Cardoso and J. M. Ezquiaga, “Can Black Holes Be Formed by Focusing Radiation?,” Phys. Rev. D111, no.4, 044049 (2025) doi:10.1103/PhysRevD.111.044049 [arXiv:2410.23347 [gr-qc]]

arXiv 2025
[2]

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P. Ball, “Black Holes Can’t Be Created by Light,” APS Physics17, 119 doi:10.1103/Physics.17.119

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´A. ´Alvarez-Dom ´ ınguez, L. J. Garay, E. Mart ´ ın-Mart ´ ınez and J. Polo-G´ omez, “Reply to Comment on “No Black Holes from Light” [arXiv:2408.06714],” [arXiv:2408.11097 [gr-qc]]

work page Pith review arXiv
[6]

Extremal Black Holes in Cosmology from Colliding Light Beams

M. Halilsoy and V. Memari, “Extremal Black Holes in Cosmology from Colliding Light Beams,” [arXiv:2411.00909 [gr-qc]]

work page Pith review arXiv
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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [5]

Can Black Holes Be Formed by Focusing Radiation?,

D. Blas, V. Cardoso and J. M. Ezquiaga, “Can Black Holes Be Formed by Focusing Radiation?,” Phys. Rev. D111, no.4, 044049 (2025) doi:10.1103/PhysRevD.111.044049 [arXiv:2410.23347 [gr-qc]]

arXiv 2025

[2] [2]

Black Holes Can’t Be Created by Light,

P. Ball, “Black Holes Can’t Be Created by Light,” APS Physics17, 119 doi:10.1103/Physics.17.119

work page doi:10.1103/physics.17.119

[3] [3]

No black holes from light

A. Loeb, “Comment on “No Black Holes from Light” [arXiv:2405.02389],” [arXiv:2408.06714 [gr-qc]]

work page Pith review arXiv

[4] [4]

Comment on "No Black Holes from Light" [arXiv:2405.02389]

´A. ´Alvarez-Dom ´ ınguez, L. J. Garay, E. Mart ´ ın-Mart ´ ınez and J. Polo-G´ omez, “Reply to Comment on “No Black Holes from Light” [arXiv:2408.06714],” [arXiv:2408.11097 [gr-qc]]

work page Pith review arXiv

[5] [6]

Extremal Black Holes in Cosmology from Colliding Light Beams

M. Halilsoy and V. Memari, “Extremal Black Holes in Cosmology from Colliding Light Beams,” [arXiv:2411.00909 [gr-qc]]

work page Pith review arXiv

[6] [7]

Collisions of Two Quanta,

G. Breit and J. A. Wheeler, “Collisions of Two Quanta,” Bull. Am. Phys. Soc. 9N2, no.2, 34.134 (1934)

work page 1934

[7] [8]

Collision of Two Light Quanta,

G. Breit and J. A. Wheeler, “Collision of Two Light Quanta,” Phys. Rev.46, no.12, 1087-1091 (1934) doi:10.1103/PhysRev.46.1087

doi:10.1103/physrev.46.1087 1934

[8] [9]

Uber das Verhalten eines Elektrons im Homogenen Elektrischen Feld nach der Relativistischen Theorie Diracs,

F. Sauter, “Uber das Verhalten eines Elektrons im Homogenen Elektrischen Feld nach der Relativistischen Theorie Diracs,” Z. Phys.69, 742-764 (1931) doi:10.1007/BF01339461

doi:10.1007/bf01339461 1931