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arxiv: 2606.23450 · v1 · pith:OZUFXLKTnew · submitted 2026-06-22 · ✦ hep-th · gr-qc

NLO Angular Impulse and Leading Singularities to all orders in spin for Kerr Black Holes

Lucas Haiashi , Gabriel Menezes This is my paper

Pith reviewed 2026-06-26 07:30 UTC · model grok-4.3

classification ✦ hep-th gr-qc
keywords Kerr black holesangular impulseleading singularitiesKMOC formalismon-shell amplitudespost-Minkowskian expansionspin effectsclassical gravitational dynamics
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0 comments X

The pith

Compact expressions for the NLO angular impulse in Kerr black hole scattering are derived from leading singularities of on-shell amplitudes, valid to all orders in spin at the integrand level.

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

The paper computes the next-to-leading order angular impulse, or spin kick, during scattering of Kerr black holes by applying the KMOC formalism to on-shell scattering amplitudes. It extracts classical observables directly via leading singularities and obtains expressions that hold to all orders in the spin variables. These expressions are shown to reduce to known results in appropriate limits while preserving the covariant spin supplementary condition and spin magnitude through 2PM order. The work also extracts a spin-resumming gravitational potential from triangle diagrams that reproduces the linear spin-orbit interaction.

Core claim

Using the KMOC formalism and on-shell scattering amplitudes, we derive compact expressions for the spin-dependent angular impulse valid to all orders in the spin variables at the integrand level, and show that these results reduce to known expressions in the appropriate limits. The conservative result preserves both the covariant spin supplementary condition and the spin magnitude through 2PM order, and the quadratic-in-spin conservative result agrees with existing radial-action results after translating between the direct KMOC spin kick and the radial-action observable. In addition, we extract the corresponding non-relativistic gravitational potential from the triangle leading singularities

What carries the argument

Leading singularities of the on-shell scattering amplitudes within the KMOC formalism, which directly extract the classical NLO angular impulse observable.

If this is right

  • The conservative NLO angular impulse preserves the covariant spin supplementary condition and spin magnitude through 2PM order.
  • The quadratic-in-spin result agrees with prior radial-action calculations once the observables are translated.
  • The gravitational potential extracted from triangle leading singularities resums spin effects to all orders while reproducing the known linear spin-orbit term.
  • The approach demonstrates that amplitude methods can compute spin-dependent classical observables without intermediate effective field theory steps.

Where Pith is reading between the lines

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

  • The all-order-in-spin integrand expressions could be integrated numerically to obtain finite observables at arbitrary spin values.
  • The method of extracting potentials from triangle singularities may generalize to higher post-Minkowskian orders for spinning binaries.
  • Agreement between KMOC and radial-action routes at quadratic spin suggests a direct dictionary between the two observables that could be tested at cubic spin order.

Load-bearing premise

The leading singularities of the on-shell scattering amplitudes directly yield the classical NLO angular impulse observable in the KMOC formalism without additional corrections or assumptions affecting the extraction.

What would settle it

An independent post-Minkowskian calculation of the NLO angular impulse at quadratic order in spin that produces a result differing from the amplitude-derived expression after accounting for the translation between KMOC spin kick and radial-action observables.

read the original abstract

We compute the next-to-leading order (NLO) angular impulse (spin kick) in the scattering of Kerr black holes using the Kosower--Maybee--O'Connell (KMOC) formalism. Our approach is based on on-shell scattering amplitudes and leading singularities, allowing for a direct extraction of classical observables from quantum amplitudes. We derive compact expressions for the spin-dependent angular impulse valid to all orders in the spin variables at the integrand level, and show that these results reduce to known expressions in the appropriate limits. We perform detailed consistency checks: the conservative result preserves both the covariant spin supplementary condition and the spin magnitude through 2PM order, and the quadratic-in-spin conservative result agrees with existing radial-action results after translating between the direct KMOC spin kick and the radial-action observable. In addition, we extract the corresponding non-relativistic gravitational potential from the triangle leading singularities, obtaining a representation that resums spin effects and reproduces the known spin-orbit interaction at linear order. Our results provide further evidence for the efficiency of amplitude-based methods in classical gravitational dynamics, and highlight the KMOC formalism as a powerful framework for computing spin-dependent observables in binary black hole scattering.

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 paper computes the next-to-leading order (NLO) angular impulse for scattering of Kerr black holes in the KMOC formalism, extracting it from on-shell scattering amplitudes via leading singularities. It derives compact integrand-level expressions for the spin-dependent angular impulse valid to all orders in spin, demonstrates reduction to known limits, verifies preservation of the covariant spin supplementary condition and spin magnitude through 2PM order for the conservative part, shows agreement of the quadratic-in-spin conservative result with radial-action results after translation, and extracts a non-relativistic gravitational potential from triangle leading singularities that resums spin effects and reproduces the known spin-orbit interaction at linear order.

Significance. If the central results hold, the work demonstrates the efficiency of amplitude methods for classical spin-dependent observables in gravitational dynamics, providing all-orders-in-spin compact expressions at the integrand level and explicit consistency checks that address common extraction issues in the KMOC approach. The reproduction of the spin-orbit potential and agreement with radial-action results after translation are notable strengths, as is the use of leading singularities for direct classical extraction.

minor comments (3)
  1. §3 (or wherever the leading-singularity extraction is detailed): clarify the precise relation between the triangle leading singularities and the non-relativistic potential extraction, including any integration measures or contour choices that ensure the spin-orbit term is isolated without higher-order contamination.
  2. The consistency checks (covariant SSC preservation, spin magnitude, and radial-action agreement) are stated for the conservative sector through 2PM; explicitly state whether these checks extend to the full NLO result including dissipative contributions or are limited to the conservative piece.
  3. Notation for the all-orders-in-spin integrand expressions: define the spin variables and their ordering conventions (e.g., with respect to the covariant SSC) at first appearance to aid readability for readers unfamiliar with the KMOC spin kick translation.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive summary of our work on the NLO angular impulse for Kerr black holes using the KMOC formalism and leading singularities, as well as for the recommendation of minor revision. No specific major comments were provided in the report.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The derivation chain relies on on-shell amplitudes and leading singularities within the KMOC formalism to extract the NLO angular impulse, with explicit reductions to known limits and external consistency checks against radial-action results and spin-orbit potentials. These steps are independent of self-referential definitions or fitted inputs renamed as predictions; the agreement with prior literature serves as validation rather than load-bearing justification. No self-citation chains, ansatze smuggled via citation, or uniqueness theorems imported from the authors' prior work appear in the provided abstract or description. The central claims remain self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Based solely on the abstract; no explicit free parameters, invented entities, or detailed axioms are identifiable beyond reliance on established formalisms.

axioms (2)
  • domain assumption The KMOC formalism extracts classical observables from quantum on-shell scattering amplitudes
    Abstract states the approach is based on the KMOC formalism allowing direct extraction of classical observables.
  • domain assumption Leading singularities in amplitudes correspond to the classical NLO angular impulse
    Abstract describes use of leading singularities for direct extraction of the classical observable.

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discussion (0)

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