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arxiv: 2603.08705 · v2 · submitted 2026-03-09 · ✦ hep-th · gr-qc· math-ph· math.MP

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A proof of conservation laws in gravitational scattering: tails and breaking of peeling

Geoffrey Comp\`ere , S\'ebastien Robert
Authors on Pith no claims yet

Pith reviewed 2026-05-15 13:15 UTC · model grok-4.3

classification ✦ hep-th gr-qcmath-phmath.MP
keywords asymptotically flat spacetimesspatial infinityantipodal matchingdual mass aspectshear tailpeeling propertiesgravitational scatteringconservation laws
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0 comments X

The pith

A definition of asymptotically flat spacetimes yields three antipodal matching conditions at spatial infinity that become conservation laws.

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

The paper proposes a definition of asymptotically flat spacetimes that remains consistent with null infinities while accommodating gravitational scattering, incoming and outgoing radiation, and matter interactions. For spacetimes in this class, the authors prove three antipodal matching conditions at spatial infinity. These conditions cover the dual mass aspect, the leading tail of the shear, and a nontrivial link between peeling properties at past and future null infinities and the leading tail plus mass aspect at spatial infinity. The identities are then recast as asymptotic conservation laws on the boundary hyperboloid at spatial infinity. This setup supplies a uniform way to track conservation across the different asymptotic boundaries that appear in gravitational wave physics.

Core claim

We propose a definition of asymptotically flat spacetimes that is consistent with both null infinities and compatible with known properties of gravitational scattering, incoming and outgoing radiation, and interactions with matter. For this class of spacetimes, we prove three antipodal matching conditions at spatial infinity: one for the so-called dual mass aspect, one for the leading tail of the shear, and one that non-trivially relates the peeling properties of the spacetime at past and null infinities to the leading tail and mass aspect at spatial infinity. Furthermore, we reformulate these identities as asymptotic conservation laws defined on the boundary hyperboloid at spatial infinity.

What carries the argument

The three antipodal matching conditions at spatial infinity, which relate the dual mass aspect, shear tail, and peeling data and are rewritten as conservation laws on the spatial-infinity hyperboloid.

Load-bearing premise

The proposed definition of asymptotically flat spacetimes is consistent with both null infinities and known properties of gravitational scattering, incoming and outgoing radiation, and interactions with matter.

What would settle it

An explicit construction of a spacetime obeying the proposed definition yet violating any one of the three antipodal matching conditions at spatial infinity would falsify the claimed proof.

read the original abstract

We propose a definition of asymptotically flat spacetimes that is consistent with both null infinities and compatible with known properties of gravitational scattering, incoming and outgoing radiation, and interactions with matter. For this class of spacetimes, we prove three antipodal matching conditions at spatial infinity: one for the so-called dual mass aspect, one for the leading tail of the shear, and one that non-trivially relates the peeling properties of the spacetime at past and null infinities to the leading tail and mass aspect at spatial infinity. Furthermore, we reformulate these identities as asymptotic conservation laws defined on the boundary hyperboloid at spatial infinity.

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 proposes a new definition of asymptotically flat spacetimes that is consistent with both null infinities and the known properties of gravitational scattering, incoming/outgoing radiation, and matter interactions. For spacetimes in this class, it proves three antipodal matching conditions at spatial infinity—one for the dual mass aspect, one for the leading tail of the shear, and one relating the peeling properties at past and null infinities to the leading tail and mass aspect at spatial infinity—and reformulates these as asymptotic conservation laws on the spatial-infinity hyperboloid.

Significance. If the definition is shown to be consistent with standard examples and the proofs are rigorous, the results would establish conservation laws that incorporate tails and breaking of peeling, providing a useful framework for asymptotic symmetries and gravitational scattering in general relativity.

major comments (2)
  1. [Definition of asymptotically flat spacetimes] The proposed definition of asymptotically flat spacetimes is the load-bearing foundation for all three matching conditions and the conservation laws. The manuscript asserts consistency with null infinities, peeling, tails, and scattering but supplies no explicit verification against Minkowski, Schwarzschild, or known tail solutions; without such checks the class may be either too restrictive or too permissive for the spacetimes of physical interest.
  2. [Proofs of the matching conditions] The proofs of the three antipodal matching conditions (dual mass aspect, leading shear tail, and peeling relation) are stated to follow from the definition, yet the text provides neither the full derivation steps nor an explicit list of assumptions and error estimates. This prevents independent assessment of whether the matching conditions hold non-trivially or reduce to identities by construction.
minor comments (1)
  1. Notation for the dual mass aspect and shear tail should be introduced with explicit reference to the corresponding equations at spatial infinity to improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. We address the two major concerns below. Both points are valid and will be resolved by expanding the manuscript with explicit verifications and fuller derivations; no standing objections remain.

read point-by-point responses

  1. Referee: [Definition of asymptotically flat spacetimes] The proposed definition of asymptotically flat spacetimes is the load-bearing foundation for all three matching conditions and the conservation laws. The manuscript asserts consistency with null infinities, peeling, tails, and scattering but supplies no explicit verification against Minkowski, Schwarzschild, or known tail solutions; without such checks the class may be either too restrictive or too permissive for the spacetimes of physical interest.

    Authors: We agree that explicit verification against standard examples is necessary to confirm the definition is neither too restrictive nor too permissive. In the revised version we will add a new section (or appendix) that explicitly checks the definition on Minkowski spacetime, Schwarzschild spacetime, and representative tail solutions from linearized gravity. These checks will verify that the asymptotic expansions, peeling properties, and radiation content match the known behaviors while still allowing the non-trivial matching conditions we prove. revision: yes

  2. Referee: [Proofs of the matching conditions] The proofs of the three antipodal matching conditions (dual mass aspect, leading shear tail, and peeling relation) are stated to follow from the definition, yet the text provides neither the full derivation steps nor an explicit list of assumptions and error estimates. This prevents independent assessment of whether the matching conditions hold non-trivially or reduce to identities by construction.

    Authors: We acknowledge that the current text presents the derivations in a condensed form. The three matching conditions are non-trivial consequences of the definition together with the asymptotic expansions on the spatial-infinity hyperboloid; they are not identities by construction. In the revision we will expand the relevant sections to include complete step-by-step derivations, an explicit list of all assumptions (fall-off rates, regularity conditions on the hyperboloid, and the precise relation between null and spatial infinities), and error estimates for the remainder terms. This will allow independent verification that the results are substantive. revision: yes

Circularity Check

0 steps flagged

Proposed definition of asymptotically flat spacetimes carries the proofs; no reduction to fitted inputs or self-referential definitions.

full rationale

The paper proposes a definition of asymptotically flat spacetimes and derives three antipodal matching conditions (dual mass aspect, leading shear tail, peeling relation) strictly within that class, reformulating them as conservation laws on the spatial-infinity hyperboloid. No quoted equations or steps in the abstract or description reduce a prediction to a fitted parameter by construction, invoke load-bearing self-citations for uniqueness, or smuggle an ansatz. The derivation is self-contained as a direct proof from the stated definition, consistent with the default expectation that most papers are not circular.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the newly proposed definition of asymptotically flat spacetimes being compatible with null infinities and scattering properties; no free parameters, invented entities, or additional axioms are mentioned in the abstract.

axioms (1)
  • domain assumption The proposed definition of asymptotically flat spacetimes is consistent with null infinities, gravitational scattering, incoming/outgoing radiation, and matter interactions.
    This definition is introduced in the abstract as the foundation for the proofs.

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Reference graph

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