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arxiv: 2605.30411 · v1 · pith:PBAXIOUKnew · submitted 2026-05-28 · ✦ hep-th · astro-ph.HE· gr-qc· hep-ph

Axions Create Singularities on Extremal Horizons

Gary T. Horowitz , Maciej Kolanowski , Grant N. Remmen , Jorge E. Santos This is my paper

Pith reviewed 2026-06-29 06:08 UTC · model grok-4.3

classification ✦ hep-th astro-ph.HEgr-qchep-ph
keywords axionsextremal black holessingular horizonsrotating black holescharged black holestidal forceshigher-derivative corrections
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The pith

Axions make the horizons of extremal rotating black holes with small charge singular.

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

The paper shows that axion scalar fields force singularities onto the horizons of black holes that are exactly extremal, rotating, and carry arbitrarily small nonzero charge. This holds for almost all values of the axion mass and its coupling to the electromagnetic field. The result matters because it identifies a mechanism by which ordinary matter fields can destroy the regularity that is usually assumed at black hole horizons in classical gravity. For large axion masses the singularities match those previously found from higher-derivative corrections to Einstein-Maxwell theory. Off exact extremality the same coupling produces very large tidal forces near the horizon and invalidates the effective field theory.

Core claim

We show that axions cause extremal black holes to have singular horizons. This is true for almost all values of the axion mass and coupling provided the black hole is rotating and has some arbitrarily small nonzero charge. When the axion mass becomes large, these singularities are related to the recently discovered singularities induced by higher-derivative corrections to the Einstein-Maxwell equations. Away from extremality, this effect produces anomalously large tidal forces in the vicinity of near-extremal horizons, causing breakdown of the effective theory.

What carries the argument

The axion field equations coupled to Einstein-Maxwell gravity on the near-horizon geometry of an extremal rotating charged black hole, which drive curvature invariants to diverge at the horizon.

If this is right

  • Singular horizons appear for almost all axion masses and couplings.
  • Large axion mass recovers the singularities previously found from higher-derivative corrections.
  • Near-extremal horizons experience anomalously large tidal forces.
  • The effective field theory breaks down near the horizon away from exact extremality.

Where Pith is reading between the lines

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

  • The same axion coupling could affect the near-horizon structure of black holes in string-theory compactifications that contain many axions.
  • Analogous singularities might arise for other periodic scalar fields with similar couplings.
  • Numerical evolution of near-extremal solutions could quantify the tidal-force growth and the scale at which the effective theory fails.

Load-bearing premise

The black hole must be exactly extremal, rotating, and possess an arbitrarily small but nonzero charge.

What would settle it

An explicit construction of a regular extremal rotating black hole with small nonzero charge in the presence of an axion with generic mass and coupling would falsify the claim.

Figures

Figures reproduced from arXiv: 2605.30411 by Gary T. Horowitz, Grant N. Remmen, Jorge E. Santos, Maciej Kolanowski.

Figure 1
Figure 1. Figure 1: S/(GQ2 ) vs J/(GQ2 ) for the near-horizon geome￾tries with g = 10 and mGQ = 7.5. For small J/(GQ2 ), three distinct branches are present. The upper branch connects to extreme Reissner-Nordström. lower branches (green diamonds and red disks) approach a non-spherical NHG in the limit J → 0. Among these, the lowest branch (red disks) ultimately connects to the NHG of an extremal Kerr black hole as J/(GQ2 ) → … view at source ↗
Figure 2
Figure 2. Figure 2: The lowest scaling dimension γ vs. J/(GQ2 ) for mGQ = 7.5, g = 10. The shaded region indicates the regime of threefold degeneracy shown in [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: Log-log plot of the tidal force Φ in Eq. (10) vs. GT Q, showing the divergence as T → 0. The dashed line is a fit using the lowest scaling dimension from the near-horizon geometry. This is for mMG = 10, Q/M = 0.75, and g = 10. g = 10 and mGM = 10, which yields a near-horizon scaling exponent of γ ≈ 0.99997. To quantify the size of tidal deformations, we compare our results with those of a Kerr-Newman black… view at source ↗
Figure 5
Figure 5. Figure 5: Relative deviation of the electric field in Eq. ( [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Convergence test quantity Ξ NxNy max as a function of J/(GM2 ), computed at several resolutions Ny (indicated on the right). The curves shown correspond to Q/M = 0.75, mGM = 1, g = 1, and Nx = 30. where we introduced Qˆ ≡ GQ, Mˆ ≡ GM, Jˆ ≡ GJ, Q˜ ≡ Q/r ˆ +, and q1(x, y) ≡ A  r+ 1 − y , x , q2(x, y) ≡ B  r+ 1 − y , x , q3(x, y) ≡ S  r+ 1 − y , x , q4(x, y) ≡ W  r+ 1 − y , x , q5(x, y) ≡ φ  r+ 1 − y… view at source ↗
Figure 7
Figure 7. Figure 7: Kretschmann scalar evaluated on the black hole horizon as a function of proper distance from the equator ( [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Left: γ as a function of mGQ for fixed g = 10 and J/(GQ2 ) = 1. Right: 1 − γ as a function of mGQ on a log-log scale. The approach to γ = 1 is consistent with a (mGQ) −2 scaling, as expected in the EFT [2]. γ as a function of mGQ for fixed g = 10 and J/(GQ2 ) = 1. In the right panel, we show 1 − γ as a function of mGQ on a log-log scale. The approach to γ = 1 is fully consistent with a (mGQ) −2 scaling, as… view at source ↗
Figure 9
Figure 9. Figure 9: Scaling dimension γ of the second-lowest mode versus J/(GQ2 ) for g = 1 and mGQ = 100. The solid black curves correspond to the analytic EFT corrections δγ(K) ± about γ (0) = 2 predicted by Ref. [2], while light red disks show our numerical data. The agreement is excellent. The apparent crossing of the analytic branches is resolved through eigenvalue repulsion, consistent with the behavior observed in Ref.… view at source ↗
read the original abstract

We show that axions cause extremal black holes to have singular horizons. This is true for almost all values of the axion mass and coupling provided the black hole is rotating and has some arbitrarily small nonzero charge. When the axion mass becomes large, these singularities are related to the recently discovered singularities induced by higher-derivative corrections to the Einstein-Maxwell equations. Away from extremality, this effect produces anomalously large tidal forces in the vicinity of near-extremal horizons, causing breakdown of the effective theory.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

0 major / 1 minor

Summary. The manuscript claims that axions induce singularities on the horizons of extremal rotating black holes carrying arbitrarily small but nonzero charge, for almost all values of the axion mass and coupling. For large axion mass the singularities are asserted to be related to those arising from higher-derivative corrections to Einstein-Maxwell theory; away from extremality the same mechanism is said to produce anomalously large tidal forces near the horizon, leading to breakdown of the effective theory.

Significance. If the central claim is rigorously derived, the result would identify a previously unnoticed mechanism by which light axionic fields destabilize extremal horizons, with direct consequences for the near-horizon geometry and the range of validity of effective field theory. The connection drawn to higher-derivative singularities supplies a potential unifying picture, and the restriction to rotating, charged, exactly extremal solutions is clearly stated.

minor comments (1)
  1. The abstract states the result without any equation or derivation; the full text must supply the explicit metric ansatz, the axion equation of motion, and the regularity analysis that establishes the singularity.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their report. The significance assessment is appreciated, and we note the recommendation is listed as uncertain with no specific major comments provided. We maintain that the central claim is rigorously derived in the manuscript, including the relation to higher-derivative singularities for large axion mass and the tidal-force analysis away from extremality.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The provided abstract and context frame the central claim as a derived result from the Einstein-axion field equations applied to extremal rotating black holes with arbitrarily small nonzero charge. No full manuscript equations, self-citations, fitted parameters, or ansatze are supplied that would permit identification of any reduction by construction. The result is scoped explicitly to the stated conditions and presented as a first-principles consequence rather than a renaming or self-referential fit. This qualifies as a self-contained theoretical derivation with no detectable circular steps.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The claim rests on the standard setup of Einstein gravity coupled to Maxwell and axion fields with mass and coupling parameters; no free parameters, invented entities, or nonstandard axioms are mentioned in the abstract.

axioms (1)
  • domain assumption Einstein-Maxwell theory coupled to an axion scalar with mass and coupling terms governs the spacetime.
    Standard effective-field-theory framework assumed for such black-hole studies.

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discussion (0)

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Reference graph

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