REVIEW
Schwinger stability of T-duality-inspired extremal black holes
High Energy Physics - Theory · Submitted 16 Sep 2026 · 16 references
Pith's verdict: Careful, honest analysis showing that the T-duality extremal black hole's vanishing near-horizon electric field suppresses the local Schwinger instability—a solid subfield contribution with acknowledged model limitations.
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Referee report
The paper
The paper claims
This paper argues that in the T-duality-inspired regular black hole, the near-horizon electric field vanishes at the lower endpoint of the extremal branch while the AdS2 radius stays finite, which eliminates the local charged-scalar…
The reading
What carries the argument
The form factor F(r) (Eq. (12)) packages the radial contribution of the regularized charge sector after the mass function is expressed in terms of the ADM mass; it modifies the extremal conditions and the near‑horizon geometry. The central object is the effective instability parameter μ²∗ (Eq. (41)), which combines the near‑horizon electric field E_H, the AdS2 radius L2, the scalar mass m, and angular momentum ℓ. The mechanism is that at the lower endpoint α=√2 the electric field E_H vanishes while L2 remains finite (√3 l0), so μ²∗ becomes manifestly negative, killing the instability.
Extended reading notes
Core claim
For the charged regular black hole obtained from the T‑duality zero‑point‑length prescription with the full form factor F(r), the extremal branch that is continuously connected to the Reissner‑Nordström limit ends at rext = √2 l0. At this endpoint the extreme charge Qext→0, the near‑horizon electric field computed from the original regularized gauge potential vanishes, and the AdS2 radius approaches √3 l0. The exact instability parameter μ²∗ (Eq. (41)) is negative at the endpoint, implying the local near‑horizon charged‑scalar Schwinger instability is absent there. In the semiclassical ℓ=0 regime the threshold ΞF diverges as α→√2⁺, so for any finite q/m the instability condition fails sufficiently close to the endpoint. This behaviour is not shared by the ABG Einstein–nonlinear‑electrodynamics black hole, whose extremal near‑horizon electric field is non‑zero and gives a finite threshold ΞABG ≃0.378.
Load-bearing premise
The effective geometry (Eq. 11) and gauge potential (Eq. 4) obtained from the static source prescription correctly represent a black hole spacetime, even though the prescription does not arise from a fully covariant action and the Maxwell stress tensor alone is not conserved.
Editorial extensions
If this is right
- For any charged scalar with a fixed finite charge‑to‑mass ratio q/m, the local Schwinger instability is absent in a neighborhood of the T‑duality extremal branch endpoint.
- The exact near‑horizon instability criterion shows that no fine‑tuning of parameters is needed to suppress the instability at the endpoint.
- In the semiclassical regime the divergent threshold implies that the usual RN‑type Schwinger instability is pushed to arbitrarily large q/m as α→√2⁺.
- The contrast with ABG demonstrates that regularity of the central singularity alone does not guarantee a divergent Schwinger barrier; the behavior depends on the specific electromagnetic sector.
- The paper's results suggest that the T‑duality regular black hole may have a stable extremal remnant at finite mass and zero charge, pending a full dynamical evolution calculation.
Reading between the lines
- If other zero‑point‑length or minimal‑length regularizations lead to a similar vanishing of the horizon electric field while keeping the throat finite, the Schwinger‑suppression effect could be a generic indicator of such spacetime structures.
- The analysis treats the charged scalar as a probe with a standard local propagator; including T‑duality corrections to the scalar field itself might shift the quantitative instability parameter, but the qualitative suppression at vanishing E_H should survive.
- The paper's endpoint state (M~1.3 l0, Q=0) could serve as a candidate final state of black hole evaporation in the T‑duality framework if Hawking emission drives the black hole along the extremal branch.
- Experimental constraints on black hole remnants or primordial black hole mass distributions could in principle rule out or favor models that predict such a stable remnant, though current data are likely too weak to distinguish.
Original abstract
We study the near-horizon charged-scalar instability associated with Schwinger pair production in the charged regular black hole geometry of the zero-point-length T-duality prescription. Using the same effective geometry and regularized gauge potential, we construct the extremal branch, its ${\rm AdS}_2 \times S^2$ near-horizon throat, and the charged-scalar instability threshold for a general form factor. For the explicit T-duality form factor the extremal branch terminates at $r_\mathrm{ext} = \sqrt2 \, l_0$, where the extremal charge and the near-horizon electric field vanish while the ${\rm AdS}_2$ radius remains finite at $\sqrt3 \, l_0$. At this endpoint the exact near-horizon instability parameter is negative. In the semiclassical regime the corresponding charge-to-mass threshold diverges as the endpoint is approached. Thus, for each fixed massive species with finite $q/m$, a sufficiently near-endpoint portion of the extremal branch is free of the local charged-scalar instability. For comparison, the Ay\'on-Beato-Garc\'ia (ABG) Einstein-nonlinear-electrodynamics solution has a nonvanishing extremal near-horizon electric field. For an additional minimally coupled charged-scalar probe, the corresponding local Schwinger threshold remains finite. Thus the divergent near-endpoint Schwinger barrier found in the T-duality branch is not a generic consequence of regularity.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
We study the near-horizon charged-scalar instability associated with Schwinger pair production in the charged regular black hole geometry of the zero-point-length T-duality prescription. Using the same effective geometry and regularized gauge potential, we construct the extremal branch, its ${\rm AdS}_2 \times S^2$ near-horizon throat, and the charged-scalar instability threshold for a general form factor. For the explicit T-duality form factor the extremal branch terminates at $r_\mathrm{ext} = \sqrt2 \, l_0$, where the extremal charge and the near-horizon electric field vanish while the ${\rm AdS}_2$ radius remains finite at $\sqrt3 \, l_0$. At this endpoint the exact near-horizon instability parameter is negative. In the semiclassical regime the corresponding charge-to-mass threshold diverges as the endpoint is approached. Thus, for each fixed massive species with finite $q/m$, a sufficiently near-endpoint portion of the extremal branch is free of the local charged-scalar instability. For comparison, the Ay\'on-Beato-Garc\'ia (ABG) Einstein-nonlinear-electrodynamics solution has a nonvanishing extremal near-horizon electric field. For an additional minimally coupled charged-scalar probe, the corresponding local Schwinger threshold remains finite. Thus the divergent near-endpoint Schwinger barrier found in the T-duality branch is not a generic consequence of regularity.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study the near-horizon charged-scalar instability associated with Schwinger pair production in the charged regular black hole geometry of the zero-point-length T-duality prescription. | contribution 0.98 | 0.89 | 0.05 | asserted 0.80 |
| s1 | Using the same effective geometry and regularized gauge potential, we construct the extremal branch, its ${\rm AdS}_2 \times S^2$ near-horizon throat, and the charged-scalar instability threshold for a general form factor. | contribution 0.71 | 0.94 | 0.06 | asserted 1.00 |
| s2 | For the explicit T-duality form factor the extremal branch terminates at $r_\mathrm{ext} = \sqrt2 \, l_0$, where the extremal charge and the near-horizon electric field vanish while the ${\rm AdS}_2$ radius remains finite at $\sqrt3 \, l_0$. | result 1.00 | 0.87 | 0.12 | asserted 1.00 |
| s3 | At this endpoint the exact near-horizon instability parameter is negative. | result 1.00 | 0.91 | 0.15 | asserted 1.00 |
| s4 | In the semiclassical regime the corresponding charge-to-mass threshold diverges as the endpoint is approached. | result 1.00 | 0.88 | 0.10 | asserted 1.00 |
| s5 | Thus, for each fixed massive species with finite $q/m$, a sufficiently near-endpoint portion of the extremal branch is free of the local charged-scalar instability. | interpretation 0.77 | 0.89 | 0.73 | asserted 1.00 |
| s6 | For comparison, the Ay\'on-Beato-Garc\'ia (ABG) Einstein-nonlinear-electrodynamics solution has a nonvanishing extremal near-horizon electric field. | background 0.77 | 0.13 | 0.03 | asserted 1.00 |
| s7 | For an additional minimally coupled charged-scalar probe, the corresponding local Schwinger threshold remains finite. | result 0.86 | 0.65 | 0.04 | asserted 1.00 |
| s8 | Thus the divergent near-endpoint Schwinger barrier found in the T-duality branch is not a generic consequence of regularity. | interpretation 0.98 | 0.77 | 0.35 | asserted 1.00 |
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Discussion
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