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arxiv: 2605.15258 · v1 · pith:F6ZYUBFZnew · submitted 2026-05-14 · ✦ hep-th · gr-qc

Generating Rotation in a Snap

Soumangsu Chakraborty , Pierre Heidmann , Gela Patashuri This is my paper

Pith reviewed 2026-05-19 15:55 UTC · model grok-4.3

classification ✦ hep-th gr-qc
keywords rotating black holessolution generating techniquesEinstein equationsfive-dimensional supergravitystatic Weyl solutionsMyers-Perry black holescoordinate transformationsnon-extremal solutions
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The pith

A purely algebraic sequence of transformations turns any static Minkowski-asymptotic solution into a rotating one without solving the Einstein equations.

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

The paper presents a method that starts with a static solution approaching flat spacetime, maps it to an AdS times sphere geometry using sigma-model transformations, applies a simple coordinate shift that introduces uniform rotation, and maps the result back to flat asymptotics. This produces a new rotating solution that satisfies the original field equations. The authors demonstrate it by recovering the Kerr black hole from Schwarzschild and the Myers-Perry solution from its static counterpart, then extend it to a linear family of static Weyl solutions to generate the first linear ansatz for multiple non-extremal rotating charged sources. The approach works in five-dimensional minimal supergravity and is claimed to apply more generally wherever AdS times sphere asymptotics and the relevant transformations exist.

Core claim

The central construction begins from an arbitrary static solution asymptotic to four- or five-dimensional Minkowski space. It is first transformed to a solution with AdS times sphere asymptotics via sigma-model transformations, a coordinate shift is performed to place the solution in a uniformly rotating frame, and the inverse transformations return it to asymptotically flat coordinates, yielding a rotating solution that satisfies the Einstein equations. This recovers the Kerr and Myers-Perry black holes directly from Schwarzschild and the corresponding static five-dimensional solution. When applied to the linear class of static Weyl solutions, the procedure produces the first linear ansatz,

What carries the argument

The coordinate shift to a uniformly rotating frame performed inside the AdS times sphere asymptotic frame, combined with the forward and inverse sigma-model transformations that change the spacetime asymptotics.

If this is right

  • Kerr black holes are recovered directly from Schwarzschild by the algebraic procedure.
  • Myers-Perry black holes are recovered from the corresponding static five-dimensional solution.
  • A linear ansatz is obtained that describes an arbitrary number of non-extremal rotating and charged sources.
  • The construction supplies a systematic route to non-extremal rotating geometries in both four and five dimensions.
  • The method extends to any theory that admits AdS times sphere geometries together with the required sigma-model transformations.

Where Pith is reading between the lines

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

  • The same algebraic detour might generate rotating solutions in theories with additional matter fields or in dimensions higher than five.
  • One could check whether the method automatically preserves conserved charges such as mass and angular momentum at each step.
  • Multi-center rotating solutions might be constructed by starting from known multi-center static seeds and applying the transformation.
  • The technique could be tested on other known static solutions to produce previously unknown rotating geometries.

Load-bearing premise

The transformed solution obtained after the coordinate shift in the AdS times sphere frame continues to satisfy the Einstein equations once it is mapped back to asymptotically flat coordinates.

What would settle it

Applying the full sequence of transformations to the Schwarzschild metric and checking whether the output is exactly the Kerr metric (or fails to solve the vacuum Einstein equations) would confirm or refute the method.

read the original abstract

We build a new technique to generate rotation from arbitrary static solutions that asymptote to four- or five-dimensional Minkowski spacetime. The method is purely algebraic and does not require solving Einstein equations. It proceeds by transforming the static solution to AdS$\times$S asymptotics, performing a coordinate shift to a uniformly rotating frame, and then transforming the solution back to asymptotically flat spacetime. We implement this construction in five-dimensional minimal supergravity, although it applies more broadly to any framework admitting AdS$\times$S geometries and relevant sigma-model transformations. As a first application, we recover simply the Kerr and Myers-Perry black holes directly from Schwarzschild black holes. We then apply the method to the linear class of static Weyl solutions and obtain the first linear ansatz describing an arbitrary number of non-extremal rotating and charged sources. This approach provides a systematic and simple route to constructing non-extremal rotating geometries in four and five dimensions.

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 / 1 minor

Summary. The manuscript presents a new algebraic technique for generating rotating black hole solutions from static ones that asymptote to Minkowski spacetime in four or five dimensions. The method involves transforming the static solution to AdS×S asymptotics, introducing rotation via a coordinate shift in that frame, and then using sigma-model transformations to map back to asymptotically flat spacetime. It is implemented in five-dimensional minimal supergravity, recovering the Kerr and Myers-Perry solutions from Schwarzschild, and applied to linear static Weyl solutions to obtain an ansatz for multiple non-extremal rotating and charged sources.

Significance. If the central claim holds, this provides a valuable systematic method for constructing non-extremal rotating geometries without solving the field equations directly. The recovery of known solutions offers initial support for the approach. Strengths include the algebraic nature and potential applicability to broader frameworks admitting AdS×S geometries and sigma-model transformations.

major comments (2)
  1. [§3] §3 (method description): The central claim that the composition of the AdS×S coordinate shift with sigma-model transformations produces a solution satisfying the original Einstein equations in flat asymptotics lacks an explicit verification or derivation step for general static inputs. While the abstract states recovery of known solutions, no concrete check (e.g., substitution into the field equations or reference to a preserved quantity) is provided beyond the Schwarzschild case.
  2. [§4] §4 (Weyl solutions application): The linear ansatz for an arbitrary number of non-extremal rotating and charged sources is presented as a first application, but the manuscript does not demonstrate that the resulting metric satisfies the field equations for multi-source configurations; this is load-bearing for the claim of obtaining the first such linear ansatz.
minor comments (1)
  1. [Abstract] The abstract claims applicability to four dimensions but the explicit implementation and examples are restricted to five-dimensional minimal supergravity; a clarifying statement on the four-dimensional case would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments. We address the two major comments point by point below, indicating the revisions we intend to make.

read point-by-point responses

  1. Referee: [§3] §3 (method description): The central claim that the composition of the AdS×S coordinate shift with sigma-model transformations produces a solution satisfying the original Einstein equations in flat asymptotics lacks an explicit verification or derivation step for general static inputs. While the abstract states recovery of known solutions, no concrete check (e.g., substitution into the field equations or reference to a preserved quantity) is provided beyond the Schwarzschild case.

    Authors: We appreciate the referee drawing attention to the need for greater explicitness. The construction proceeds by a sequence of operations each of which maps solutions of the equations of motion to solutions: the change to AdS×S asymptotics is a coordinate redefinition, the uniform rotation is a diffeomorphism in that frame, and the subsequent sigma-model transformations are symmetries of the five-dimensional minimal supergravity action. Consequently the composition preserves the property of being a solution. This is verified concretely by the recovery of the Kerr and Myers-Perry metrics from Schwarzschild, both of which are known to satisfy the Einstein equations. To make the general argument transparent we will insert a short subsection in §3 that recalls the relevant sigma-model symmetries and notes that the inverse transformations return the solution to the original theory while preserving the equations. revision: yes

  2. Referee: [§4] §4 (Weyl solutions application): The linear ansatz for an arbitrary number of non-extremal rotating and charged sources is presented as a first application, but the manuscript does not demonstrate that the resulting metric satisfies the field equations for multi-source configurations; this is load-bearing for the claim of obtaining the first such linear ansatz.

    Authors: We agree that an explicit check for multi-source configurations would strengthen the presentation. Because the static Weyl solutions satisfy the equations and our algebraic procedure maps solutions to solutions, the resulting rotating multi-source metric satisfies the field equations by construction. The linearity of the ansatz follows from the linearity of the static seed and the fact that the transformations act parametrically on the Weyl potentials. Nevertheless, to address the referee’s concern directly we will add a brief verification for the two-source case in the revised §4, confirming that the metric satisfies the relevant sigma-model equations (or, equivalently, the Einstein equations) for that configuration. revision: partial

Circularity Check

0 steps flagged

Algebraic construction is self-contained with independent verification on known solutions

full rationale

The paper describes a purely algebraic procedure that maps static Minkowski-asymptotic solutions to AdS×S asymptotics, applies a coordinate shift, and maps back via sigma-model transformations. It explicitly recovers the Kerr and Myers-Perry solutions from Schwarzschild as a consistency check and then produces a new linear ansatz for rotating Weyl solutions. No quoted step reduces a claimed prediction or central result to a fitted parameter, self-definition, or load-bearing self-citation chain; the transformations are presented as preserving the equations by construction within each frame, and the method is independent of re-solving the Einstein equations for the target rotating geometries.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no explicit free parameters, axioms, or invented entities; the method relies on standard sigma-model transformations and AdS×S geometries assumed to exist in the target theories.

pith-pipeline@v0.9.0 · 5686 in / 1089 out tokens · 37512 ms · 2026-05-19T15:55:39.819340+00:00 · methodology

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