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arxiv: 2601.18048 · v3 · submitted 2026-01-26 · ✦ hep-th

Recognition: 2 theorem links

· Lean Theorem

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

Mois\'es Bravo-Gaete , Jhony A. Herrera-Mendoza , Julio Oliva , Xiangdong Zhang
Authors on Pith no claims yet

Pith reviewed 2026-05-16 11:31 UTC · model grok-4.3

classification ✦ hep-th
keywords five-dimensional black holesLifshitz asymptoticsrotating black holesaxionic chargesholographic superconductorsChern-Simons termsdynamical exponent
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The pith

Five-dimensional rotating Lifshitz black holes can be supported by both electric and axionic charges.

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

The paper constructs an explicit family of five-dimensional black holes that are asymptotically Lifshitz and rotate while carrying electric and axionic charges. These solutions are obtained by solving the Einstein equations coupled to a dilaton field, gauge fields, and axionic scalars with generalized Chern-Simons terms. The authors verify that the solutions obey the first law of black hole thermodynamics and derive the associated Smarr relation for a range of the dynamical exponent z. As an application, they examine a holographic superconductor in this background and find that rotation suppresses the scalar condensate while a larger dynamical exponent strengthens the superconducting phase.

Core claim

The central discovery is a new family of exact five-dimensional charged and rotating asymptotically Lifshitz black holes. The spacetime solves the Einstein equations coupled to a dilaton, two Abelian gauge fields, and axionic scalars supplemented by two generalized Chern-Simons terms. The configuration is characterized by a range of the free dynamical exponent z and possesses nontrivial thermodynamical parameters, where the first law of black hole thermodynamics is verified and the corresponding Smarr relation derived. These solutions provide the first explicit family of five-dimensional rotating Lifshitz black holes supported simultaneously by electric and axionic charges.

What carries the argument

The metric and field ansatz with generalized Chern-Simons terms that admits exact solutions with Lifshitz asymptotics, rotation, and both charges for a continuous range of the dynamical exponent z.

If this is right

  • The first law of black hole thermodynamics holds for these solutions.
  • A Smarr relation follows from the thermodynamic parameters of the family.
  • Increasing the rotation parameter suppresses the scalar condensate in the dual holographic superconductor.
  • Increasing the dynamical critical exponent enhances the superconducting order.

Where Pith is reading between the lines

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

  • These backgrounds could model rotating non-relativistic condensed matter systems through holographic duality.
  • The rotation-induced suppression of condensation offers a tunable parameter for phase transitions in the dual theory.
  • Similar ansatze may yield solutions in other dimensions or with additional matter fields.

Load-bearing premise

A specific metric and field ansatz combined with generalized Chern-Simons terms allows exact solutions with the required Lifshitz scaling and charges for a continuous range of the dynamical exponent.

What would settle it

Direct substitution of the proposed metric and fields into the Einstein equations to verify whether the equations hold identically for a chosen value of the dynamical exponent z.

Figures

Figures reproduced from arXiv: 2601.18048 by Jhony A. Herrera-Mendoza, Julio Oliva, Mois\'es Bravo-Gaete, Xiangdong Zhang.

Figure 1
Figure 1. Figure 1: FIG. 1. Graphical representation of the function [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The condensation profiles for the operator [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Real (left) and imaginary (right) parts of the conductivity as functions of the frequency for different values of the [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Real (left) and imaginary (right) parts of the conductivity as functions of the frequency for different values of the [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
read the original abstract

In this work, we construct a new family of exact five-dimensional charged and rotating asymptotically Lifshitz black holes. The spacetime solves Einstein equations coupled to a dilaton, two Abelian gauge fields, and axionic scalars supplemented by two generalized Chern-Simons terms. This configuration is characterized by a range of the free dynamical exponent $z$ and possesses nontrivial thermodynamical parameters, where we verify the first law of black hole thermodynamics and derive the corresponding Smarr relation. As an application of this new gravitational background, we then investigate a holographic superconductor in the rotating Lifshitz background. We study the condensation of the scalar operator and the AC conductivity of the dual system. These results show that increasing the rotation parameter suppresses the condensate and weakens the superconducting phase, while increasing the dynamical critical exponent enhances the superconducting order. To the best of our knowledge, these solutions provide the first explicit family of five-dimensional rotating Lifshitz black holes supported simultaneously by electric and axionic charges.

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 / 2 minor

Summary. The paper constructs a new family of exact five-dimensional rotating asymptotically Lifshitz black holes carrying both electric and axionic charges. The solutions arise from a direct metric and field ansatz in Einstein gravity coupled to a dilaton, two Abelian gauge fields, axionic scalars, and generalized Chern-Simons terms. The configurations are shown to solve the field equations for a continuous range of the dynamical exponent z, to possess a regular horizon, and to satisfy the first law of black-hole thermodynamics together with the corresponding Smarr relation. As an application, the backgrounds are used to study holographic superconductivity, where the effects of the rotation parameter and z on scalar condensation and AC conductivity are analyzed.

Significance. If the explicit solutions are correct, the work supplies the first known family of five-dimensional rotating Lifshitz black holes supported by both electric and axionic charges. This fills a concrete gap in the literature and supplies new gravitational backgrounds for holographic studies of condensed-matter systems with Lifshitz scaling and rotation. The direct verification of thermodynamic consistency and the concrete holographic results on how rotation suppresses condensation while larger z enhances the order parameter constitute clear strengths of the manuscript.

minor comments (2)
  1. [Section 2] The explicit metric functions, dilaton profile, and gauge-field components obtained after solving the reduced ODEs should be written out in full (perhaps in an appendix) so that independent verification of the Einstein equations and thermodynamic identities is immediate.
  2. [Section 4] In the holographic-superconductor section, the precise boundary conditions imposed on the scalar field and the definition of the order parameter should be stated explicitly, together with the numerical method used to extract the critical temperature.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the careful reading and positive evaluation of our manuscript. The referee summary accurately captures our main results: the construction of the first known family of five-dimensional rotating asymptotically Lifshitz black holes carrying both electric and axionic charges, the direct verification that the solutions satisfy the field equations for a range of z, the confirmation of the first law and Smarr relation, and the holographic superconductivity analysis demonstrating that rotation suppresses scalar condensation while larger z enhances the order parameter. Since no specific major comments were raised, we have no individual points to address.

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper constructs its five-dimensional rotating Lifshitz black hole solutions via an explicit metric and field ansatz (including dilaton, two gauge fields, axions, and generalized Chern-Simons terms) that directly reduces the modified Einstein equations to solvable ODEs, yielding exact expressions with Lifshitz asymptotics, regular horizons, and independent charges for a continuous range of z. Thermodynamic relations such as the first law and Smarr formula are then verified by direct substitution of the obtained quantities rather than by any redefinition or fitting procedure. No load-bearing steps reduce to self-definition, fitted inputs renamed as predictions, or self-citation chains; the derivation remains self-contained against the input ansatz and the field equations.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the existence of an ansatz that solves the modified Einstein equations exactly for Lifshitz asymptotics; the only notable free parameter is the dynamical exponent z whose allowed range is determined by the equations.

free parameters (1)
  • dynamical exponent z
    Free parameter controlling Lifshitz scaling that must lie in a specific range for the rotating charged solutions to exist.
axioms (1)
  • domain assumption Einstein equations coupled to a dilaton, two Abelian gauge fields, axionic scalars and two generalized Chern-Simons terms
    The spacetime is required to satisfy these modified field equations.

pith-pipeline@v0.9.0 · 5481 in / 1223 out tokens · 58230 ms · 2026-05-16T11:31:55.892631+00:00 · methodology

discussion (0)

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

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matches
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supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
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unclear
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Reference graph

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