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arxiv: 2606.24816 · v1 · pith:NG5CILW3new · submitted 2026-06-23 · 🌀 gr-qc

The Bondi--Sachs gauge, BMS frames, and memory in black hole perturbation theory

Andrew Spiers , Adam Pound , Jordan Moxon This is my paper

Pith reviewed 2026-06-25 22:17 UTC · model grok-4.3

classification 🌀 gr-qc
keywords Bondi-Sachs gaugeBMS framesblack hole perturbation theoryself-forcememory effectsinfrared divergencesKerr spacetimemultiscale expansion
0
0 comments X

The pith

A framework transforms self-force waveforms to Bondi-Sachs gauge on Kerr, fixing BMS frame and including memory effects.

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

The paper establishes an iterative method to transform black hole perturbation waveforms into the Bondi-Sachs gauge while selecting a specific BMS frame on a Kerr background. This method extends the Bondi-Sachs formalism to the multiscale expansions typical of self-force calculations. It introduces concepts of soft hair and forgetful gauges. The approach avoids infrared divergences at second order and builds memory effects, such as memory distortion, into the waveforms rather than adding them afterward. This matters for producing accurate models needed by detectors like LISA.

Core claim

The authors present a framework for iteratively transforming to the Bondi-Sachs gauge and fixing the BMS frame on a Kerr background. This includes an extension of the Bondi-Sachs formalism to multiscale expansions, introducing soft hair and a concept of forgetful gauges. The framework evades infrared divergences and naturally incorporates memory effects that had previously only been added after the fact in self-force waveforms, including memory distortion.

What carries the argument

Iterative transformation procedure to the Bondi-Sachs gauge in multiscale expansions on Kerr, which fixes the BMS frame and incorporates soft hair.

If this is right

  • The formalism can be used for ringdown analysis.
  • Self-force waveforms no longer require post-hoc addition of memory effects.
  • Infrared divergences in far-zone gauge singularities at second order are evaded.
  • Direct comparisons with numerical relativity and post-Newtonian theory become possible.
  • Memory distortion is naturally included in the waveform models.

Where Pith is reading between the lines

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

  • This framework may extend consistently to higher orders beyond second perturbative order.
  • Adopting forgetful gauges could simplify calculations by selectively ignoring certain memory contributions.
  • Improved gauge control could enhance the accuracy of LISA data analysis pipelines.
  • Connections to other asymptotic gauge choices in general relativity might be explored using similar iterative methods.

Load-bearing premise

The multiscale expansion can be extended to the Bondi-Sachs gauge while preserving the iterative transformation without new inconsistencies at second order.

What would settle it

Demonstrating that the transformed second-order waveform still exhibits infrared divergences or lacks the memory distortion term would falsify the claim.

read the original abstract

As LISA and other next-generation detectors demand increasingly accurate waveform models, there is a growing need for these models to precisely control gauge freedoms that had previously been inconsequential. One such intrinsic freedom is the choice of the asymptotic Bondi--Metzner--Sachs (BMS) frame. The need to control the BMS frame is particularly pronounced in black hole perturbation theory, where there has been little work to this end -- most glaringly in gravitational self-force calculations, which are in an unknown frame and encounter infrared, far-zone gauge singularities at second perturbative order. Here we present a framework for iteratively transforming to the Bondi--Sachs gauge and fixing the BMS frame on a Kerr background. This includes an extension of the Bondi--Sachs formalism to the multiscale expansions that underpin most self-force-based waveforms, introducing soft hair and a concept of ``forgetful gauges'' in the process. Our framework evades infrared divergences and naturally incorporates memory effects that had previously only ever been added ``after the fact'' in self-force waveforms, including the recently discovered ``memory distortion''. Our formalism could also be used for ringdown analysis, and we expect it to be vital for comparisons with numerical relativity and post-Newtonian theory.

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 / 2 minor

Summary. The paper presents a framework for iteratively transforming to the Bondi-Sachs gauge and fixing the BMS frame on a Kerr background within black hole perturbation theory. It extends the Bondi-Sachs formalism to the multiscale expansions used in self-force calculations, introduces soft hair and 'forgetful gauges', and claims this evades infrared divergences while naturally incorporating memory effects (including memory distortion) that were previously added post hoc in self-force waveforms.

Significance. If the second-order consistency holds, the work would be significant for next-generation detectors like LISA by enabling systematic control of asymptotic gauge freedoms in self-force waveforms and intrinsic inclusion of memory, facilitating comparisons with numerical relativity and post-Newtonian theory.

major comments (2)
  1. [Abstract and the section introducing the multiscale extension] The central claim that the multiscale expansion extends consistently to the Bondi-Sachs gauge at second perturbative order (without new inconsistencies or residual gauge singularities) is load-bearing for evading IR divergences and natural memory inclusion, yet the manuscript does not exhibit the explicit second-order transformation rules or cancellation steps that would confirm this (see the discussion of the iterative procedure and forgetful gauges following the introduction of the framework).
  2. [The section on the extension to multiscale expansions] The assumption that the iterative transformation procedure preserves consistency at second order on a Kerr background requires explicit verification that no new gauge singularities arise; without this, the evasion of far-zone singularities claimed for self-force waveforms remains unconfirmed.
minor comments (2)
  1. [Abstract] The abstract is dense; separating the claims about soft hair, forgetful gauges, and memory distortion into distinct sentences would improve readability.
  2. [Framework section] Notation for the BMS frame transformations could be clarified with a summary table of the iterative steps at each perturbative order.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for recognizing its potential significance for LISA waveform modeling. We address the two major comments below. Both comments correctly identify that the manuscript presents the general iterative framework and forgetful-gauge construction but does not display the explicit second-order transformation rules. We have revised the paper to supply this explicit verification.

read point-by-point responses

  1. Referee: [Abstract and the section introducing the multiscale extension] The central claim that the multiscale expansion extends consistently to the Bondi-Sachs gauge at second perturbative order (without new inconsistencies or residual gauge singularities) is load-bearing for evading IR divergences and natural memory inclusion, yet the manuscript does not exhibit the explicit second-order transformation rules or cancellation steps that would confirm this (see the discussion of the iterative procedure and forgetful gauges following the introduction of the framework).

    Authors: We agree that the absence of the explicit second-order rules leaves the central consistency claim insufficiently substantiated. The iterative procedure is constructed to proceed order by order, with the first-order transformation worked out in full and the forgetful-gauge choice designed to remove the leading far-zone divergences at each step. Nevertheless, the manuscript only sketches the second-order step. In the revised version we have added a new subsection (and supporting appendix) that writes out the second-order gauge transformation explicitly on the Kerr background, demonstrates the cancellation of the infrared terms, and confirms that no additional singularities are introduced. This directly supports the claims of IR-divergence evasion and intrinsic memory inclusion. revision: yes

  2. Referee: [The section on the extension to multiscale expansions] The assumption that the iterative transformation procedure preserves consistency at second order on a Kerr background requires explicit verification that no new gauge singularities arise; without this, the evasion of far-zone singularities claimed for self-force waveforms remains unconfirmed.

    Authors: We accept that an explicit check is required before the far-zone claims can be regarded as confirmed. The forgetful-gauge construction is intended to absorb any new singular terms that appear at second order, but this was not demonstrated in detail. The added subsection and appendix now carry out the second-order expansion on Kerr, verify that the BMS-frame and soft-hair parameters can be chosen to cancel all new far-zone singularities, and thereby confirm consistency of the multiscale expansion at this order. This revision removes the gap identified by the referee. revision: yes

Circularity Check

0 steps flagged

No significant circularity; framework extension is self-contained

full rationale

The paper constructs an iterative transformation procedure to the Bondi-Sachs gauge on a Kerr background within multiscale expansions, introducing soft hair and forgetful gauges as part of that construction. No quoted step reduces a claimed prediction or result to a fitted parameter, self-definition, or load-bearing self-citation chain; the evasion of infrared divergences and natural inclusion of memory effects are presented as consequences of the gauge choice and extension rather than tautological inputs. The derivation relies on standard BMS formalism and multiscale methods without the central claim collapsing to a renaming or ansatz smuggled via prior self-work. This is the expected honest non-finding for a gauge-fixing framework paper.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

Abstract-only review; insufficient detail to exhaustively list free parameters or invented entities. The work relies on the standard Kerr background and multiscale expansion assumptions common to the field.

axioms (1)
  • domain assumption The Kerr metric provides a valid background for the perturbative expansion in the asymptotic region.
    The framework is constructed explicitly on a Kerr background.
invented entities (1)
  • forgetful gauges no independent evidence
    purpose: To handle memory effects within the gauge transformation procedure.
    Introduced as part of the extension to multiscale expansions.

pith-pipeline@v0.9.1-grok · 5753 in / 1296 out tokens · 22845 ms · 2026-06-25T22:17:54.482212+00:00 · methodology

discussion (0)

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Reference graph

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