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arxiv: 2511.00632 · v2 · submitted 2025-11-01 · ✦ hep-th · gr-qc

Weyl double copy in Lifshitz spacetimes

Gokhan Alkac , Mehmet Kemal Gumus , Mehmet Ali Olpak This is my paper

Pith reviewed 2026-05-18 01:21 UTC · model grok-4.3

classification ✦ hep-th gr-qc
keywords double copyWeyl double copyKerr-Schild double copyLifshitz black holesregularization prescriptionspacetime solutionsgravity-gauge correspondence
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The pith

A regularization prescription restores consistency between the Kerr-Schild and Weyl double copies for Lifshitz black holes.

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

This paper tests whether a regularization step can make the Weyl double copy agree with the Kerr-Schild double copy when both are applied to Lifshitz black hole solutions. These spacetimes are known to create mismatches between the two formulations of the double copy. The authors apply the prescription to three distinct solutions drawn from the literature and report that agreement is recovered in every case. A sympathetic reader cares because the double copy links gravitational fields to gauge-theory fields, so methods that extend the link to new families of solutions widen its reach.

Core claim

The paper establishes that the regularization prescription remains valid for three Lifshitz black hole solutions, each carrying a different novel feature, and that this step restores consistency between the Kerr-Schild double copy and the Weyl double copy in all three examples.

What carries the argument

The regularization prescription applied to the Weyl double copy, which adjusts the computation so that the resulting gauge-theory data matches the Kerr-Schild data for these spacetimes.

If this is right

  • The prescription succeeds for solutions that differ in their asymptotic or horizon properties.
  • No change to the basic double-copy map itself is required once the regularization is included.
  • The same adjustment can be carried over to other gravitational solutions that previously resisted a clean Weyl double copy.
  • Consistency between the two copies now holds across a wider class of non-asymptotically flat backgrounds.

Where Pith is reading between the lines

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

  • If the prescription proves general, it could be applied next to other non-standard black-hole families that show similar mismatches.
  • The result suggests a practical route for extending double-copy techniques into holographic models that use Lifshitz geometries.
  • An analytic demonstration that the regularization always works, rather than case-by-case checks, would strengthen the claim.

Load-bearing premise

That three specific Lifshitz black hole solutions chosen from the literature are representative enough to indicate the prescription works in general.

What would settle it

Discovery of one Lifshitz black hole solution where the same regularization step still leaves the Kerr-Schild and Weyl double copies inconsistent.

read the original abstract

Lifshitz black hole solutions pose particular challenges for reconciling the two main formulations of the classical double copy: the Kerr-Schild double copy and the Weyl double copy. Recent work has suggested that consistency between the two can be restored, in certain cases, only by adopting a regularization prescription in the Weyl double copy. In this paper, we test this prescription on three examples from the literature, each with a distinct novel feature, and show that the prescription remains valid in all cases.

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 / 3 minor

Summary. The manuscript tests a regularization prescription intended to restore consistency between the Kerr-Schild and Weyl formulations of the classical double copy when applied to Lifshitz black hole solutions. The authors examine three specific solutions drawn from the existing literature, each selected for a distinct novel feature, and report that the prescription succeeds in all three cases.

Significance. If the reported agreement holds under scrutiny, the work supplies concrete evidence that the regularization approach extends the reach of double-copy techniques into non-asymptotically flat geometries relevant to holographic condensed-matter models. The study is framed as an incremental consistency check rather than a general derivation, so its primary value lies in broadening the domain of existing prescriptions while avoiding new free parameters or ad-hoc constructions.

minor comments (3)
  1. The abstract states that the prescription 'remains valid in all cases' but does not define the quantitative criterion (exact matching, agreement up to a given order, or vanishing of a specific discrepancy) used to reach this conclusion.
  2. A brief table or explicit comparison of the regularized Weyl tensor components against the Kerr-Schild copy for at least one of the three examples would make the agreement easier to verify without requiring the reader to reconstruct the full calculation.
  3. The introduction would benefit from a short paragraph clarifying why the three chosen Lifshitz solutions are representative of the broader class rather than merely convenient examples already present in the literature.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive and constructive report, which accurately summarizes our work as a consistency check of the regularization prescription for the Weyl double copy in Lifshitz black hole backgrounds. We appreciate the recognition that the study extends double-copy techniques to non-asymptotically flat geometries without introducing new parameters.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper conducts an empirical consistency check by applying a regularization prescription (sourced from recent external work) to three specific Lifshitz black hole solutions drawn from the existing literature. The central result—that the prescription restores agreement between Kerr-Schild and Weyl double copies in all tested cases—is a verification against independent prior examples rather than a derivation that reduces to the paper's own fitted inputs, self-citations, or ansatz. No load-bearing step equates a prediction to a parameter defined inside the work; the analysis remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper relies on standard assumptions of classical double-copy constructions and the validity of the chosen Lifshitz black-hole metrics from prior literature; no new free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption The Kerr-Schild and Weyl double-copy formulations are expected to agree for physically reasonable spacetimes once a suitable regularization is applied.
    Invoked to motivate the consistency check performed on the three examples.

pith-pipeline@v0.9.0 · 5599 in / 1185 out tokens · 21260 ms · 2026-05-18T01:21:59.769753+00:00 · methodology

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Forward citations

Cited by 2 Pith papers

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

  1. The Smarr Formula is Gauss's Law: A Kerr-Schild Single-Copy Perspective

    hep-th 2026-05 unverdicted novelty 6.0

    The Smarr formula is structurally identical to the single-copy Gauss's law for Kerr-Schild black holes, with the AdS pressure-volume term arising from gauge background subtraction.

  2. Minisuperspace Double Copy in Lifshitz Spacetimes

    hep-th 2026-04 unverdicted novelty 6.0

    A radial operator extracted from the reduced gravitational dynamics in Lifshitz spacetimes directly reproduces the Maxwell operator for the temporal single-copy field without using equations of motion.

Reference graph

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