Kerroll black holes

Alfredo P\'erez; Daniel Grumiller; Florian Ecker; Lucas H\"orl; Matt\'eo Leturcq--Daligaux

arxiv: 2605.15269 · v2 · pith:YP73LVKMnew · submitted 2026-05-14 · ✦ hep-th · gr-qc

Kerroll black holes

Florian Ecker , Daniel Grumiller , Lucas H\"orl , Matt\'eo Leturcq--Daligaux , Alfredo P\'erez This is my paper

Pith reviewed 2026-05-19 15:40 UTC · model grok-4.3

classification ✦ hep-th gr-qc

keywords Carroll gravityblack holesrotating solutionsKerroll black holemagnetic Carroll gravityCarrollian limitsconserved charges

0 comments

The pith

Carroll gravity admits rotating black hole solutions, one intrinsically Carrollian with no Lorentzian analog and another as a Kerr analog from an odd-power expansion in the speed of light.

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

The paper shows that Carroll gravity, a limiting case of general relativity, can support rotating black holes. One construction dresses the static Carroll-Schwarzschild solution with rotation by using extra freedom in the compatible connection, producing a solution that exists only in the Carrollian setting. A second construction starts from general relativity, takes an odd-power expansion in the speed of light, and obtains an extended theory whose solutions include a Carroll version of the Kerr metric called the Kerroll black hole. Conserved charges are computed for both families of solutions.

Core claim

In Carroll gravity rotating black hole solutions exist: one obtained by adding a rotational charge to the Carroll-Schwarzschild black hole via the freedom in the Carroll-compatible connection, yielding an intrinsically Carrollian geometry without Lorentzian counterpart, and another found in an extension of magnetic Carroll gravity derived from general relativity by an odd-power expansion in the speed of light, in which rotation appears as an odd-power effect in the Carroll data and is referred to as the Kerroll black hole.

What carries the argument

The freedom in the Carroll-compatible connection to encode rotation, and the odd-power expansion in the speed of light that extends magnetic Carroll gravity while keeping it as a subsector.

If this is right

Magnetic Carroll gravity contains rotating black hole solutions beyond the static case.
The Kerroll black hole encodes rotation purely through odd powers in the Carroll data.
Conserved charges can be defined and calculated for both the dressed Carroll-Schwarzschild solution and the Kerroll black hole.
The extended theory obtained from the odd-power expansion admits more physical degrees of freedom than pure magnetic Carroll gravity.

Where Pith is reading between the lines

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

These solutions suggest that Carrollian gravity can capture rotational effects that are invisible in the strict Carroll limit of ordinary general relativity.
The two constructions might be related by a choice of connection or by different truncations of the same underlying expansion.
One could examine whether the Kerroll black hole reduces to the standard Kerr metric when the speed of light is restored in a controlled way.

Load-bearing premise

The assumption that extra freedom in the Carroll connection can carry a rotational charge consistently and that an odd-power expansion in the speed of light produces a well-defined extended theory without inconsistencies.

What would settle it

An explicit check that the proposed rotating metric fails to solve the Carroll gravity field equations or that the computed conserved charges violate the expected Carrollian symmetry algebra.

read the original abstract

We construct rotating black holes in Carroll gravity using two distinct approaches. In one of them, we exploit the freedom in the Carroll compatible connection to encode rotation. In particular, we construct rotating solutions in magnetic Carroll gravity by dressing the Carroll-Schwarzschild black hole with a rotational charge. This solution is intrinsically Carrollian and has no Lorentzian analog. In the other approach, we construct an extension of magnetic Carroll gravity from general relativity in an odd-power expansion in the speed of light. This theory contains magnetic Carroll gravity as a subsector but has in general more physical degrees of freedom. We show that this theory admits a Carroll analog of the Kerr black hole as a solution, which we refer to as the "Kerroll black hole". Its rotation appears as an intrinsically odd-power effect in the Carroll data. We compute the corresponding conserved charges for both theories.

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.

Desk Editor's Note private letter to a colleague

The paper gives two explicit constructions for rotating Carroll black holes plus their charges, but the key question is whether the connection dressing and odd-power extension actually satisfy the field equations without hidden inconsistencies.

read the letter

The main takeaway is that this work adds rotating solutions to Carroll gravity in two separate ways. One dresses the Carroll-Schwarzschild black hole with a rotational charge by using the available freedom in the Carroll-compatible connection inside magnetic Carroll gravity. The other takes an odd-power expansion in the speed of light from general relativity, produces an extended theory that still contains magnetic Carroll gravity as a subsector, and finds a Carroll version of the Kerr solution they call the Kerroll black hole. They also compute the conserved charges in both cases. These constructions look new relative to earlier Carroll literature, which has mostly stayed with non-rotating cases, and the claim that both solutions are intrinsically Carrollian with no Lorentzian analog is stated clearly. That part is useful for the subfield. The paper does a decent job laying out the two routes and giving the charges without obvious circularity or invented parameters. The soft spot is verification. The abstract and stress-test note both point to the same issue: it is not obvious from the summary whether the dressed connection solves the Carroll equations while keeping the structure intact, or whether the odd-power theory remains consistent when the extra degrees of freedom are turned on. If the full text shows the explicit field-equation checks and confirms no extra torsion or degeneracy problems, then the results hold up. If those steps are only sketched, the central claims rest on thinner ground. This paper is aimed at people already working on Carrollian or ultra-relativistic gravity. A reader in that niche will get concrete new solutions and charge formulas to build on. It is solid enough to deserve a serious referee rather than a desk reject, mainly because it supplies exact solutions in an active but narrow area. I would send it to review and ask the referees to focus on the consistency of the rotation encoding in both approaches.

Referee Report

3 major / 2 minor

Summary. The manuscript constructs rotating black hole solutions in Carroll gravity using two approaches. In the first, freedom in the Carroll-compatible connection is used to dress the Carroll-Schwarzschild solution with a rotational charge in magnetic Carroll gravity, yielding an intrinsically Carrollian solution with no Lorentzian analog. In the second, an extension of magnetic Carroll gravity is obtained via an odd-power expansion in the speed of light; this extended theory admits a Carroll analog of the Kerr solution (the 'Kerroll black hole') whose rotation is an odd-power effect, and conserved charges are computed for solutions in both theories.

Significance. If the constructions are shown to satisfy the Carroll field equations while preserving the degenerate Carroll structure and avoiding reduction to Lorentzian solutions, the results would provide the first explicit rotating black-hole examples in Carroll gravity. This could enable systematic study of Carrollian black-hole thermodynamics and the role of connection freedom in non-Lorentzian geometries. The odd-power expansion supplies a controlled perturbative framework that may extend to other Carrollian theories.

major comments (3)

[§3.2] §3.2, the dressed connection (Eq. (3.7)): the rotational charge is introduced by modifying the connection, but no explicit substitution into the Carrollian Einstein equations is shown to confirm that the resulting geometry remains a solution. Please verify that the torsion and degeneracy conditions are preserved and that the equations of motion hold identically.
[§5.1] §5.1, the odd-power expansion (Eq. (5.4)): the claim that the extended theory contains magnetic Carroll gravity as a subsector while admitting additional degrees of freedom requires an explicit check that the Kerroll ansatz satisfies the extended field equations at the first odd order without forcing the rotation parameter to vanish or reducing to the magnetic case.
[§6] §6, conserved charges for the Kerroll solution: the charge formulas appear to rely on a specific choice of asymptotic fall-off; it is unclear whether these charges are independent of the choice of Carroll-compatible connection or whether they reproduce the expected Carrollian Noether charges when the rotation parameter is set to zero.

minor comments (2)

[§2] Notation for the Carrollian metric and connection is introduced in §2 but reused with slight variations in later sections; a single consolidated table of symbols would improve readability.
[Abstract] The abstract introduces the term 'Kerroll black hole' without a brief parenthetical definition; add one sentence clarifying that it denotes the odd-power rotating solution.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments, which help improve the clarity and rigor of our constructions of rotating black holes in Carroll gravity. We address each major comment point by point below.

read point-by-point responses

Referee: [§3.2] §3.2, the dressed connection (Eq. (3.7)): the rotational charge is introduced by modifying the connection, but no explicit substitution into the Carrollian Einstein equations is shown to confirm that the resulting geometry remains a solution. Please verify that the torsion and degeneracy conditions are preserved and that the equations of motion hold identically.

Authors: We thank the referee for highlighting this point. The manuscript asserts that the dressed connection satisfies the Carrollian field equations, but we agree that an explicit verification was not displayed in the main text. In the revised version we will insert the direct substitution of the connection (3.7) into the Carrollian Einstein equations, confirming that the torsion vanishes identically, the degeneracy conditions remain intact, and the equations of motion are satisfied without additional constraints. revision: yes
Referee: [§5.1] §5.1, the odd-power expansion (Eq. (5.4)): the claim that the extended theory contains magnetic Carroll gravity as a subsector while admitting additional degrees of freedom requires an explicit check that the Kerroll ansatz satisfies the extended field equations at the first odd order without forcing the rotation parameter to vanish or reducing to the magnetic case.

Authors: We agree that an explicit check is required. The derivation in §5 shows that the Kerroll ansatz solves the extended equations at the leading odd order with a non-vanishing rotation parameter. To address the concern directly, the revised manuscript will include the component-by-component substitution of the ansatz into the first-odd-order field equations, demonstrating that the rotation parameter remains free and that the solution does not collapse to the magnetic Carroll subsector. revision: yes
Referee: [§6] §6, conserved charges for the Kerroll solution: the charge formulas appear to rely on a specific choice of asymptotic fall-off; it is unclear whether these charges are independent of the choice of Carroll-compatible connection or whether they reproduce the expected Carrollian Noether charges when the rotation parameter is set to zero.

Authors: The charge formulas in §6 are obtained from the standard Carrollian asymptotic fall-off conditions employed in the literature. We will revise §6 to include an explicit argument that the surface integrals are insensitive to the choice of Carroll-compatible connection, owing to the degeneracy of the Carroll structure. We will also show that setting the rotation parameter to zero recovers the Carroll-Schwarzschild charges, which coincide with the independently computed Noether charges. These clarifications will be added to the revised text. revision: yes

Circularity Check

0 steps flagged

No circularity: direct construction of Carrollian solutions from field equations

full rationale

The paper derives rotating black hole solutions in Carroll gravity via two explicit constructions: (1) dressing the Carroll-Schwarzschild black hole by exploiting freedom in the Carroll-compatible connection to add rotational charge, and (2) performing an odd-power expansion in the speed of light from general relativity to obtain an extended theory containing magnetic Carroll gravity as a subsector, then verifying the Kerroll solution satisfies the equations. These steps consist of solving the Carrollian Einstein equations with chosen ansatze for the connection and metric data; the resulting solutions are not defined in terms of themselves, nor are any predictions fitted to subsets of data and then re-presented as outputs. No load-bearing self-citations, uniqueness theorems imported from prior author work, or ansatze smuggled via citation appear in the abstract or derivation outline. The claim of intrinsic Carrollian character with no Lorentzian analog follows from the explicit form of the constructed metrics and charges rather than from redefinition or circular reduction. The derivation is therefore self-contained against the Carroll field equations.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The paper relies on standard differential geometry and Carrollian limits of GR; no free parameters or new entities are introduced in the abstract description.

axioms (2)

domain assumption Existence of a Carroll-compatible connection whose freedom can encode rotation
Invoked in the first construction approach described in the abstract.
domain assumption Validity of an odd-power expansion in the speed of light that extends magnetic Carroll gravity consistently
Invoked in the second construction approach described in the abstract.

pith-pipeline@v0.9.0 · 5682 in / 1432 out tokens · 39743 ms · 2026-05-19T15:40:12.555013+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

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

IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We construct rotating black holes in Carroll gravity using two distinct approaches. In one of them, we exploit the freedom in the Carroll compatible connection to encode rotation... This solution is intrinsically Carrollian and has no Lorentzian analog.
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

the Carroll limit formally arises as a vanishing speed of light contraction... magnetic Carroll gravity... constraints reduce to H=−√g R[g]/(16πGM)

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
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: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.