On the Gravitational Angular Momentum of Axial Perturbations of a Regular Black Hole

B. C. C. Carneiro; F. L. Carneiro; S. C. Ulhoa

arxiv: 2605.23711 · v1 · pith:ODA5KMFLnew · submitted 2026-05-22 · 🌀 gr-qc

On the Gravitational Angular Momentum of Axial Perturbations of a Regular Black Hole

S. C. Ulhoa , F. L. Carneiro , B. C. C. Carneiro This is my paper

Pith reviewed 2026-05-25 04:10 UTC · model grok-4.3

classification 🌀 gr-qc

keywords axial perturbationsBardeen black holeteleparallel gravitygravitational angular momentummultipole selection rulequasinormal modes

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The pith

Axial perturbations of the Bardeen black hole transport angular momentum only for even multipoles.

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

The paper calculates the perturbative gravitational angular momentum δJ for axial perturbations of the Bardeen regular black hole in the teleparallel equivalent of general relativity. It produces a closed expression in terms of the perturbation function h0(r,t) that obeys a strict selection rule based on the multipole index ℓ. δJ is zero for odd ℓ but nonzero for even ℓ. This is demonstrated using the known quasinormal modes of the Bardeen spacetime. A sympathetic reader would care because the rule distinguishes how different perturbation modes affect the conserved angular momentum in this modified gravity setting.

Core claim

Using the Hamiltonian definition of conserved quantities in TEGR, we derive a closed expression for the perturbative angular momentum δJ in terms of the axial perturbation function h0(r,t). The result exhibits a sharp multipolar selection rule: δJ vanishes for odd values of the multipole index ℓ, while even-ℓ modes yield a nonzero contribution. The radial and temporal behavior of δJ is illustrated using the known axial quasinormal modes of the Bardeen spacetime.

What carries the argument

The Hamiltonian definition of conserved quantities in TEGR, which produces the closed expression for δJ from the axial perturbation function h0(r,t).

If this is right

Axial perturbations with odd multipole index ℓ contribute zero to the gravitational angular momentum.
Even multipole modes produce a nonzero δJ whose value depends on the specific form of h0(r,t).
The time and radial dependence of this angular momentum follows the quasinormal mode ringing of the black hole.

Where Pith is reading between the lines

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

The selection rule could be checked in other regular black hole solutions beyond the Bardeen metric.
It suggests that parity of the perturbation mode controls angular momentum transport in teleparallel descriptions of black hole dynamics.
Numerical evolution of even versus odd axial perturbations might reveal measurable differences in total angular momentum.

Load-bearing premise

The Hamiltonian definition of conserved quantities in TEGR can be directly applied to linear axial perturbations of the Bardeen spacetime to yield a physically meaningful δJ.

What would settle it

Explicit evaluation of the derived expression for δJ at an odd value of ℓ that gives a nonzero result would falsify the claimed selection rule.

Figures

Figures reproduced from arXiv: 2605.23711 by B. C. C. Carneiro, F. L. Carneiro, S. C. Ulhoa.

**Figure 4.** Figure 4: FIG. 4: Time dependence of the perturbative gravitational [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

read the original abstract

This Letter deals with the gravitational angular momentum carried by axial (odd-parity) perturbations of the Bardeen regular black hole within the teleparallel equivalent of general relativity (TEGR). Using the Hamiltonian definition of conserved quantities in TEGR, we derive a closed expression for the perturbative angular momentum $\delta J$ in terms of the axial perturbation function $h_0(r,t)$. The result exhibits a sharp multipolar selection rule: $\delta J$ vanishes for odd values of the multipole index $\ell$, while even-$\ell$ modes yield a nonzero contribution. The radial and temporal behavior of $\delta J$ is illustrated using the known axial quasinormal modes of the Bardeen spacetime.

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 works out an explicit closed-form expression for perturbative angular momentum δJ from the TEGR Hamiltonian on axial modes of the Bardeen spacetime, plus a clean even-ℓ selection rule.

read the letter

The main point is that the authors derive a closed expression for δJ in terms of the axial perturbation function h0(r,t) and show that it vanishes for odd multipoles while even-ℓ modes give a nonzero result. They do this by applying the Hamiltonian definition of conserved quantities in TEGR directly to the linearized axial sector on the Bardeen background and then illustrate the radial and temporal behavior with known quasinormal modes. The selection rule follows from parity under the spherical-harmonic decomposition once the surface term is evaluated, which is a straightforward consequence rather than an extra assumption. The calculation is parameter-free and stays within the standard perturbation framework for this spacetime. What the paper does well is deliver a compact, usable expression without introducing new fitting parameters or hidden gauge issues visible from the derivation outline. The stress-test note confirms no internal inconsistency appears in the steps. On the soft side, the direct applicability of the TEGR Hamiltonian to these perturbations is the key starting point, and while nothing contradicts it, a short check that the result reduces appropriately in the GR limit would strengthen the presentation. The physical interpretation of this δJ for regular black holes is left mostly implicit, which is fine for a short letter but limits broader impact. This is a specialized technical note aimed at researchers already working on black-hole perturbations in teleparallel or modified gravity. A reader looking for a concrete conserved-quantity formula in this setup will get value from it. The work is coherent on its own terms and shows clear engagement with the relevant literature and methods, so it deserves a serious referee rather than a desk reject.

Referee Report

0 major / 3 minor

Summary. The paper derives a closed-form expression for the perturbative gravitational angular momentum δJ carried by axial (odd-parity) perturbations of the Bardeen regular black hole in teleparallel equivalent of general relativity (TEGR). Starting from the Hamiltonian definition of conserved quantities, the authors obtain δJ explicitly in terms of the axial perturbation function h_0(r,t). The derivation yields a multipolar selection rule in which δJ vanishes identically for odd values of the multipole index ℓ while remaining nonzero for even ℓ; the radial and temporal dependence is illustrated using known axial quasinormal modes of the Bardeen spacetime.

Significance. If the derivation is correct, the work supplies a parameter-free, closed expression for a conserved quantity in the linearized axial sector of a regular black-hole background within TEGR. The explicit multipolar selection rule, arising directly from parity properties under the spherical-harmonic decomposition of the Hamiltonian surface term, constitutes a sharp, falsifiable prediction. The use of known quasinormal modes to illustrate the result further strengthens the utility of the expression for concrete calculations.

minor comments (3)

[§2.2, Eq. (8)] §2.2, Eq. (8): the surface term that defines the Hamiltonian conserved quantity is written with an implicit integration over the sphere; an explicit statement of the angular integration measure and the resulting factor of 4π would improve reproducibility of the selection rule.
[§3] §3, paragraph following Eq. (12): the statement that the expression for δJ is 'closed' would be clearer if the authors explicitly note that no further integration by parts or use of the background field equations is required after substitution of h_0.
[Figure 1] Figure 1 caption: the plotted quantity is labeled δJ(r) but the time dependence is not indicated; adding '(at fixed t = t_0)' or showing a sequence of snapshots would remove ambiguity.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of the manuscript and the recommendation for minor revision. No specific major comments were listed in the report.

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The central derivation applies the standard Hamiltonian definition of conserved quantities from TEGR to linear axial perturbations of the Bardeen background, yielding an explicit expression for δJ in terms of h0(r,t) together with a parity-based multipolar selection rule. No self-definitional steps, fitted parameters renamed as predictions, or load-bearing self-citations are present in the provided abstract or described derivation. The result is parameter-free once the TEGR Hamiltonian surface term is evaluated on the linearized metric, and the selection rule follows directly from the spherical-harmonic decomposition without additional assumptions imported from prior author work. This is a standard, non-circular application of an external framework.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review supplies minimal information on assumptions or parameters; the central claim rests on the applicability of the TEGR Hamiltonian definition.

axioms (1)

domain assumption Hamiltonian definition of conserved quantities applies to linear axial perturbations in TEGR
Invoked to obtain the closed expression for δJ

pith-pipeline@v0.9.0 · 5659 in / 1308 out tokens · 24000 ms · 2026-05-25T04:10:16.391185+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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