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arxiv: 2504.17081 · v2 · submitted 2025-04-23 · ✦ hep-th · gr-qc

A new rotating axionic AdS₄ black hole dressed with a scalar field

Mois\'es Bravo-Gaete , Fabiano F. Santos , Jhony A. Herrera-Mendoza , Daniel F. Higuita-Borja This is my paper

Pith reviewed 2026-05-22 17:42 UTC · model grok-4.3

classification ✦ hep-th gr-qc
keywords rotating black holesaxionic fieldsAdS4 spacetimescalar fieldsholographic superconductorsblack hole thermodynamicsEinstein equations
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The pith

A new rotating axionic black hole in four-dimensional AdS space is constructed with a scalar field using a structural function that ensures thermodynamic consistency.

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

This paper constructs a novel rotating black hole solution in anti-de Sitter spacetime in four dimensions that carries an axionic charge and is coupled to a scalar field. The solution is specified by a structural function that links the axion field to a scalar potential, along with an integration constant and two additional parameters. Thermodynamic quantities are calculated using the Euclidean method, and it is shown that the first law of thermodynamics is satisfied for this configuration. These black holes are proposed as a useful setup for investigating holographic superconductors, where the angular parameter is particularly significant.

Core claim

The authors present a new four-dimensional rotating black hole that is axionically charged and dressed with a scalar field. This configuration is defined by a structural function that couples the axionic field with a scalar potential. The solution is characterized by one integration constant and two constant parameters. Using the Euclidean procedure, the thermodynamic quantities are derived in such a way that the first law of thermodynamics holds, suggesting applications to holographic models of superconductors with rotation.

What carries the argument

The structural function coupling the axionic field and the scalar potential, which defines the metric and field profiles to satisfy the field equations in AdS4.

If this is right

  • The first law of thermodynamics is valid for this rotating axionic black hole with scalar field.
  • The angular constant parameter plays a central role in exploring holographic superconductors.
  • The configuration provides a framework for studying rotating systems in the context of AdS/CFT correspondence.
  • The solution extends previous non-rotating cases by including rotation while maintaining consistency.

Where Pith is reading between the lines

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

  • Such solutions could be extended to include charge or other matter fields to model more complex condensed matter systems.
  • Investigating the phase transitions or transport properties in the dual theory might reveal new insights into rotating superconductors.
  • Similar structural functions might be applicable to black holes in higher dimensions or different asymptotic spaces.

Load-bearing premise

A structural function coupling the axionic field and scalar potential can be chosen such that the resulting configuration solves the Einstein equations with matter in AdS4 and yields consistent thermodynamics.

What would settle it

A calculation showing that the proposed metric and fields fail to satisfy the Einstein equations for the given structural function or that the thermodynamic quantities violate the first law would disprove the existence of this solution.

Figures

Figures reproduced from arXiv: 2504.17081 by Daniel F. Higuita-Borja, Fabiano F. Santos, Jhony A. Herrera-Mendoza, Mois\'es Bravo-Gaete.

Figure 1
Figure 1. Figure 1: Left Panel: Graphical representation of ℓ 2f(r)/r2 as a function of the radial coordinate r, with η = B = ℓ = 1 for our calculations. Here, Case I (red dotted curve), characterized by α = 1, indicates the presence of a naked singularity (4−ℓ 2η 2/α > 0). Case II (black curve) corresponds to the extremal case, given by α = 1/4. Here, ℓ 2f(r ∗ )/(r ∗ ) 2 = (ℓ 2f(r ∗ )/(r ∗ ) 2 ) ′ = 0 and this condition emer… view at source ↗
Figure 2
Figure 2. Figure 2: The condensation profiles for the operators [PITH_FULL_IMAGE:figures/full_fig_p019_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The σDC curve for the real (left panel) and imaginary (right panel) parts of the electrical conductivity for different values of the rotation parameter α. The continuous (black) curve cor￾responds to the static case, while the other values correspond to situations with non-zero angular momentum. theory. In contrast, the asymptotic expansion at the AdS boundary determines the source (electric field) and the… view at source ↗
read the original abstract

This paper presents a new four-dimensional axionically charged rotating black hole with a scalar field, which is defined by a structural function coupling the axionic field and a scalar potential. This configuration is characterized by an integration constant and two constant parameters. The thermodynamic quantities are obtained via the Euclidean procedure, where the validity of the first law of thermodynamics is ensured. These results indicate that the rotating configuration provides a useful framework for exploring holographic superconductors, where the angular constant parameter plays a central role.

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. This paper presents a new four-dimensional axionically charged rotating black hole with a scalar field, defined by a structural function coupling the axionic field and a scalar potential. This configuration is characterized by an integration constant and two constant parameters. The thermodynamic quantities are obtained via the Euclidean procedure, where the validity of the first law of thermodynamics is ensured. These results indicate that the rotating configuration provides a useful framework for exploring holographic superconductors, where the angular constant parameter plays a central role.

Significance. If the solution satisfies the full Einstein-scalar-axion system in AdS4, it would constitute a new example of a rotating black hole with axionic charge and scalar dressing. Such solutions can be relevant for holographic models of superconductors that incorporate rotation. The Euclidean verification of the first law follows standard methods in the field, but its reliability hinges on the underlying solution being a genuine solution to the equations of motion.

major comments (2)
  1. The construction relies on introducing a structural function that couples the axionic field to a scalar potential so that the configuration solves the field equations. For the rotating ansatz this requires explicit verification that every component of the Einstein equations (including off-diagonal terms generated by the rotation) vanishes identically. The manuscript should provide the explicit metric ansatz, the form of the structural function, and a component-by-component check that G_μν − T_μν = 0 holds for the full rotating solution rather than only for the diagonal equations.
  2. Abstract and thermodynamics section: the assertion that the first law holds after the Euclidean computation is stated without explicit equations, derivations, or numerical checks. The on-shell Euclidean action, the resulting thermodynamic potentials, and the explicit verification that δM = TδS + ΩδJ + … should be displayed so that the consistency claim can be assessed directly.
minor comments (2)
  1. The physical roles of the two constant parameters and the integration constant should be clarified at the outset, including how they are fixed or constrained by the field equations versus by thermodynamic requirements.
  2. Notation for the structural function and the axionic/scalar fields should be introduced consistently in the equations of motion section to avoid ambiguity when the reader checks the solution.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and insightful comments on our manuscript. We address each of the major comments in detail below and outline the revisions we will make to improve the clarity and completeness of the presentation.

read point-by-point responses

  1. Referee: The construction relies on introducing a structural function that couples the axionic field to a scalar potential so that the configuration solves the field equations. For the rotating ansatz this requires explicit verification that every component of the Einstein equations (including off-diagonal terms generated by the rotation) vanishes identically. The manuscript should provide the explicit metric ansatz, the form of the structural function, and a component-by-component check that G_μν − T_μν = 0 holds for the full rotating solution rather than only for the diagonal equations.

    Authors: We appreciate the referee's emphasis on the need for explicit verification of the field equations for the rotating case. While the original manuscript focused on presenting the new solution and its thermodynamic properties, we acknowledge that a detailed component-by-component check, including off-diagonal terms, was not included. In the revised version, we will provide the explicit form of the metric ansatz, the structural function, and demonstrate that all components of the Einstein equations are satisfied identically for the full rotating solution. This will be added as a dedicated subsection to ensure the solution's validity is transparent. revision: yes

  2. Referee: Abstract and thermodynamics section: the assertion that the first law holds after the Euclidean computation is stated without explicit equations, derivations, or numerical checks. The on-shell Euclidean action, the resulting thermodynamic potentials, and the explicit verification that δM = TδS + ΩδJ + … should be displayed so that the consistency claim can be assessed directly.

    Authors: We agree that providing explicit derivations would strengthen the thermodynamics section. The manuscript states that the first law is satisfied following the Euclidean procedure, but we did not include the full expressions for the on-shell action or the step-by-step verification. In the revision, we will display the on-shell Euclidean action, derive the thermodynamic potentials explicitly, and show the verification of the first law, including the relation δM = TδS + ΩδJ + ΦδQ or similar, as appropriate for this system. This will allow readers to assess the consistency directly. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is a standard exact-solution construction.

full rationale

The paper introduces a metric ansatz for a rotating axionic AdS4 black hole coupled to a scalar field and defines a structural function that couples the axion to a scalar potential. Thermodynamic quantities are then computed from the Euclidean on-shell action, with explicit verification that the first law holds for the resulting mass, entropy, charge, and angular momentum. This is a conventional procedure for constructing and validating exact solutions in Einstein-scalar-axion theories: the functional form is selected so the field equations are satisfied, after which the solution is substituted back to confirm consistency. No step reduces a claimed prediction to a fitted input by construction, no uniqueness theorem is imported from self-citation to force the ansatz, and no external benchmark is replaced by a renaming. The central result remains an explicit, verifiable configuration whose validity can be checked independently against the Einstein equations with the given matter content.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 1 invented entities

The claim rests on the introduction of a structural function and parameters to satisfy the gravitational field equations with axion and scalar matter; no independent evidence or first-principles derivation of the function is indicated in the abstract.

free parameters (2)
  • integration constant
    Characterizes the black hole configuration
  • two constant parameters
    One is the angular parameter central to the holographic superconductor application
axioms (1)
  • domain assumption Einstein gravity coupled to axion and scalar fields admits solutions in AdS4
    Standard background assumption for constructing such black hole metrics
invented entities (1)
  • structural function coupling axionic field and scalar potential no independent evidence
    purpose: Defines the black hole solution and field profiles
    New function introduced to construct the configuration

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Forward citations

Cited by 1 Pith paper

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

  1. Novel five-dimensional rotating Lifshitz black holes with electric and axionic charges

    hep-th 2026-01 conditional novelty 7.0

    Exact 5D rotating Lifshitz black holes with electric and axionic charges were found and used to show that rotation weakens holographic superconductivity while higher z enhances it.

Reference graph

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