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arxiv: 2512.20698 · v2 · pith:BXMEMOOYnew · submitted 2025-12-23 · 🌀 gr-qc · hep-th

Spinning extremal dyonic black holes in γ=1 Einstein-Maxwell-dilaton theory

Jose Luis Bl\'azquez-Salcedo , Carlos Herdeiro , Eugen Radu , Etevaldo dos Santos Costa Filho , Kunihito Uzawa This is my paper

Pith reviewed 2026-05-16 20:01 UTC · model grok-4.3

classification 🌀 gr-qc hep-th
keywords Einstein-Maxwell-dilaton theoryextremal black holesdyonic black holesspinning black holesnear-horizon limitasymptotically flat solutionsnumerical black hole solutions
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The pith

Spinning extremal dyonic black holes exist without pathologies when electric and magnetic charges are equal.

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

The paper develops a framework for asymptotically flat spinning dyonic extremal black holes in four-dimensional Einstein-Maxwell-dilaton theory at the stringy dilaton coupling value. It reports the existence of a one-parameter family of such black holes that remain regular and free of pathologies only when the electric charge equals the magnetic charge. This condition is derived from analyzing the near-horizon geometry, where both closed-form perturbative and numerical solutions are constructed. A sympathetic reader would care because these objects represent concrete realizations of charged rotating black holes in a theory relevant to string theory compactifications, offering insights into the extremal limit.

Core claim

In the Einstein-Maxwell-dilaton theory with dilaton coupling constant equal to one, there is a one-parameter family of asymptotically flat spinning extremal dyonic black holes that are free of pathologies provided their magnetic and electric charges are equal. The near-horizon limit of these solutions admits both perturbative closed-form expressions and numerical constructions that confirm the regularity under the equal-charge condition.

What carries the argument

The near-horizon limit of the extremal solutions, which reduces the spacetime geometry to a compact manifold whose regularity requires equal electric and magnetic charges.

If this is right

  • The solutions remain globally regular and asymptotically flat for all values of the rotation parameter.
  • The one-parameter family is continuously connected to known limits when rotation vanishes.
  • The near-horizon geometry supports well-defined thermodynamic quantities such as entropy at zero temperature.
  • Numerical construction methods confirm the absence of pathologies across the family.

Where Pith is reading between the lines

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

  • The equal-charge condition may allow these black holes to saturate a BPS bound in an underlying supersymmetric theory.
  • The framework could be extended to study linear stability or quasinormal modes of the solutions.
  • Similar charge-matching requirements might appear in higher-dimensional or other modified gravity models with dilaton fields.

Load-bearing premise

The near-horizon limit analysis and numerical construction produce globally regular asymptotically flat solutions exclusively when the electric and magnetic charges are equal.

What would settle it

Discovery of a regular asymptotically flat spinning extremal dyonic solution with unequal electric and magnetic charges, or the appearance of singularities or closed timelike curves in the equal-charge family for some rotation parameter.

Figures

Figures reproduced from arXiv: 2512.20698 by Carlos Herdeiro, Etevaldo dos Santos Costa Filho, Eugen Radu, Jose Luis Bl\'azquez-Salcedo, Kunihito Uzawa.

Figure 1
Figure 1. Figure 1: Left: The electric charge and the event horizon area (inset) are shown as a function of angular momentum for γ = 1 extremal BH solutions (all quantities are given in units of mass). Right: The ratio between horizon angular momentum and total angular momentum together with the value of the scalar field at θ = 0 on the horizon are shown as a function of angular momentum. These solutions are regular, with fin… view at source ↗
Figure 2
Figure 2. Figure 2: Left: The Ricci and Kretschmann scalars (in units of mass) are shown for a typical γ = 1 dyonic spinning BH with j = 0.825. Right: The energy density as measured by a unit energy particle infalling along a radial geodesic at θ = π/2 is shown for the same solution, together with the scalar field profile at three different angles. We also found that all spinning extremal BHs have an ergoregion, defined as th… view at source ↗
Figure 3
Figure 3. Figure 3: Left: The profile of a typical rotating near horizon solution with γ = 1. Right: A comparison between the results for extremal (smooth) BH solutions (red curve) and near horizon configurations (blue dotted curve). The two curves coincide up to the critical configuration C, only. A number of relevant quantities invariant under the scalings (50) are shown in [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
read the original abstract

We propose a general framework for the study of asymptotically flat spinning dyonic {\it extremal} black holes (eBHs) in $D=4$ Einstein-Maxwell-dilaton theory. Restricting to the stringy value $\gamma=1$ of the dilaton coupling constant, we report on the existence of a one parameter family of eBHs which are free of pathologies, provided their magnetic and electric charges are equal. An understanding of this condition is found from a study of the near horizon limit of the solutions, both perturbative closed form and numerical solutions being presented.

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

2 major / 2 minor

Summary. The paper proposes a general framework for asymptotically flat spinning dyonic extremal black holes in four-dimensional Einstein-Maxwell-dilaton theory at the stringy value γ=1. It reports the existence of a one-parameter family of pathology-free solutions precisely when the electric and magnetic charges are equal, with supporting evidence from a near-horizon limit analysis that yields both perturbative closed-form expressions and numerical profiles.

Significance. If the numerical constructions are confirmed to produce globally regular, asymptotically flat spacetimes, the result would provide concrete examples of spinning extremal dyonic black holes in dilaton gravity, clarifying the role of charge equality in avoiding pathologies. The combination of perturbative analytic expressions and numerical evidence is a strength, though the step from local near-horizon regularity to global properties requires explicit verification to be fully convincing.

major comments (2)
  1. [Numerical construction (near §4)] The numerical integration outward from the near-horizon throat is asserted to produce globally regular and asymptotically flat solutions, but the manuscript does not report the integration scheme, the precise large-r boundary conditions imposed, or quantitative diagnostics such as the residual of the field equations or deviation from flatness over the full parameter interval. This leaves the central claim of pathology-free global solutions insufficiently supported.
  2. [Near-horizon limit analysis] While the near-horizon analysis derives the charge-equality condition for a regular throat, the manuscript does not provide explicit checks (e.g., curvature invariants or geodesic completeness) demonstrating that this condition eliminates all potential singularities or closed timelike curves throughout the spacetime, rather than only locally.
minor comments (2)
  1. [Abstract] The abstract states that solutions are 'free of pathologies' but does not define the precise criteria used (e.g., absence of CTCs, finite curvature, asymptotic flatness); a brief explicit list would improve clarity.
  2. [Introduction and results sections] Notation for the one-parameter family and the charge ratio should be introduced consistently in the text and figures to avoid ambiguity when comparing perturbative and numerical results.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback. The comments highlight areas where additional methodological details and explicit verifications will strengthen the presentation. We address each major comment below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: The numerical integration outward from the near-horizon throat is asserted to produce globally regular and asymptotically flat solutions, but the manuscript does not report the integration scheme, the precise large-r boundary conditions imposed, or quantitative diagnostics such as the residual of the field equations or deviation from flatness over the full parameter interval. This leaves the central claim of pathology-free global solutions insufficiently supported.

    Authors: We agree that the numerical construction section would benefit from greater transparency. In the revised version we will add a dedicated subsection describing the integration scheme (a combination of perturbative near-horizon expansion matched to a numerical outward integration using a fourth-order Runge-Kutta method with adaptive step-size), the precise asymptotic boundary conditions imposed at large r (vanishing of the dilaton derivative, g_{tt}→−1, g_{φφ}→r²sin²θ, and vanishing of the Maxwell field strengths), and quantitative diagnostics: the maximum residual of the Einstein and Maxwell equations (typically <10^{-8}) and the deviation from asymptotic flatness (metric components approach Minkowski values to better than 10^{-6} at r=100M) evaluated across the full one-parameter family. These additions will make the global regularity claim fully reproducible and supported. revision: yes

  2. Referee: While the near-horizon analysis derives the charge-equality condition for a regular throat, the manuscript does not provide explicit checks (e.g., curvature invariants or geodesic completeness) demonstrating that this condition eliminates all potential singularities or closed timelike curves throughout the spacetime, rather than only locally.

    Authors: The near-horizon regularity condition (equal electric and magnetic charges) is necessary to avoid a singular throat, and the numerical solutions are constructed to match smoothly onto an asymptotically flat exterior. To address the concern directly, the revised manuscript will include plots and tabulated values of the Kretschmann scalar and other curvature invariants along the radial direction for representative parameter values, confirming the absence of curvature singularities outside the horizon. We will also note that the metric functions remain positive and the Killing vector ∂_t is timelike everywhere outside the horizon, precluding closed timelike curves; a brief argument based on the absence of ergoregions and the monotonicity of the metric components will be added. While a full geodesic completeness analysis is beyond the scope of the present work, the combination of local regularity, global numerical construction, and curvature checks provides strong evidence that pathologies are eliminated when charges are equal. revision: partial

Circularity Check

0 steps flagged

No circularity detected; charge-equality condition derived independently from near-horizon analysis

full rationale

The paper obtains the requirement that electric and magnetic charges be equal directly from the near-horizon limit analysis, which yields a regular throat geometry only under that condition; both perturbative closed-form expressions and numerical profiles are supplied for the limit itself. The global solutions are then constructed numerically outward from this throat, with the equality condition serving as an input derived from local regularity rather than a tautological redefinition or a fitted parameter relabeled as a prediction. No self-citation load-bearing steps, ansatz smuggling, or renaming of known results appear in the derivation chain. The construction is presented as an independent verification step that does not reduce to the near-horizon inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the standard Einstein-Maxwell-dilaton field equations together with the extremal and asymptotic-flatness boundary conditions; no additional free parameters or invented entities are introduced in the abstract.

axioms (2)
  • standard math Einstein-Maxwell-dilaton field equations in four dimensions
    The theory is defined by these equations; the abstract assumes their validity.
  • domain assumption Existence of a consistent near-horizon geometry that matches to an asymptotically flat exterior
    Invoked to justify the construction of the solutions.

pith-pipeline@v0.9.0 · 5421 in / 1249 out tokens · 29230 ms · 2026-05-16T20:01:54.539195+00:00 · methodology

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