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arxiv: 2602.19186 · v2 · pith:PRRVWS3Inew · submitted 2026-02-22 · 🌀 gr-qc · hep-th

Propagation effects of Lorentz violation in gravitational waves

A. A. Ara\'ujo Filho , N. Heidari , Iarley P. Lobo This is my paper

Pith reviewed 2026-05-21 13:23 UTC · model grok-4.3

classification 🌀 gr-qc hep-th
keywords gravitational wavesLorentz violationStandard Model Extensionbirefringencedispersion relationwave propagationpolarization mixing
0
0 comments X

The pith

Lorentz-violating operators rescale gravitational wave speed and induce birefringence.

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

This paper examines how isotropic Lorentz- and diffeomorphism-violating operators in the linearized gravitational sector of the Standard Model Extension affect the propagation of gravitational waves. The modified dispersion relation rescales the propagation speed and introduces helicity-dependent corrections that produce birefringence and polarization mixing. The authors derive the retarded Green function for the altered wave operator and obtain explicit expressions for the gravitational waveform generated by matter sources such as binary black holes. These changes alter the observed strain through shifted times and amplitude effects, and existing data from events like GW170817 are used to bound the coefficients without adding new propagating degrees of freedom.

Core claim

The combined effects of the CPT-even dimension-four coefficient and the CPT-odd dimension-five coefficient modify the gravitational wave dispersion relation, rescaling the propagation speed and adding helicity-dependent terms that cause birefringence and polarization mixing. This occurs without introducing additional propagating degrees of freedom. The retarded Green function associated with the modified wave operator is derived, and explicit expressions for the gravitational waveform from matter sources are obtained, including alterations to the strain from binary black hole systems via shifted retarded times, amplitude rescaling, and higher derivative corrections to the quadrupole formula.

What carries the argument

The modified wave operator that incorporates the isotropic contributions of the dimension-four and dimension-five Lorentz-violating coefficients and yields the retarded Green function for computing altered gravitational waveforms.

If this is right

  • The gravitational waveform from binary black hole systems exhibits shifted retarded times, amplitude rescaling, and higher derivative corrections to the quadrupole formula.
  • Helicity-dependent corrections produce birefringence and polarization mixing in the detected strain.
  • Constraints from GW170817/GRB 170817A and GWTC-3 propagation tests translate into bounds on the specific isotropic coefficients using polarization consistency arguments.
  • The tensorial gravitational radiation sector remains intact without additional propagating degrees of freedom.

Where Pith is reading between the lines

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

  • These modifications provide a concrete way to test Lorentz invariance in the gravitational sector using the polarization content of future multi-messenger events.
  • The absence of new modes means any detected effects would appear as corrections to the standard two tensor polarizations rather than as extra signals.
  • The derived Green function offers a calculational tool that could be applied to other source types or combined with matter interactions in extended models.

Load-bearing premise

The analysis assumes that the effects are dominated by isotropic contributions from the CPT-even dimension-four and CPT-odd dimension-five operators and that observational constraints from gravitational wave events can be mapped directly onto bounds for these specific coefficients.

What would settle it

A high-precision measurement of arrival times and polarizations from a distant gravitational wave event that shows identical propagation speeds and no helicity-dependent differences for the two tensor modes would falsify significant effects from these operators.

Figures

Figures reproduced from arXiv: 2602.19186 by A. A. Ara\'ujo Filho, Iarley P. Lobo, N. Heidari.

Figure 1
Figure 1. Figure 1: Illustration of a two-body black-hole system viewed in the barycentric frame. The compact [PITH_FULL_IMAGE:figures/full_fig_p015_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Waveform h + xx(t, r) as a function of time t for a representative configuration with ω = 0.5, r = 20, µ = 1, and l0 = 1. The signal incorporates the combined effects of the Lorentz–violating coefficients ˚k (4) (I) and ˚k (5) (V ) , and displays a clear attenuation characterized by a gradual decrease of the amplitude as time evolves. When the CPT–odd coefficient ˚k (5) (V ) is switched on (here ˚k (5) (V … view at source ↗
Figure 3
Figure 3. Figure 3: Impact of the Lorentz–violating operators [PITH_FULL_IMAGE:figures/full_fig_p020_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Parametric plot of the helicity (+) waveform in the ( [PITH_FULL_IMAGE:figures/full_fig_p020_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Transverse deformation of a ring of freely falling test particles induced by a gravitational wave. [PITH_FULL_IMAGE:figures/full_fig_p021_5.png] view at source ↗
read the original abstract

We investigate the propagation of gravitational waves in the presence of Lorentz- and diffeomorphism-violating operators within the linearized gravitational sector of the Standard Model Extension. Focusing on isotropic contributions, we analyze the combined effects of the CPT-even dimension-four coefficient $\mathring{k}^{(4)}_{(I)}$ and the CPT-odd dimension-five coefficient $\mathring{k}^{(5)}_{(V)}$ on tensorial gravitational radiation. The modified dispersion relation induces both a rescaling of the propagation speed and helicity-dependent corrections, leading to birefringence and polarization mixing without introducing additional propagating degrees of freedom. We derive the retarded Green function associated with the modified wave operator and obtain explicit expressions for the gravitational waveform generated by matter sources. As an application, we examine a binary black hole system and show how Lorentz violation alters the observed strain through shifted retarded times, amplitude rescaling, and higher derivative corrections to the quadrupole formula. Using GW170817/GRB 170817A, published GWTC-3 propagation tests, and conservative polarization consistency arguments, we translate existing observational constraints into bounds on $\mathring{k}^{(4)}_{(I)}$ and $\mathring{k}^{(5)}_{(V)}$.

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

1 major / 2 minor

Summary. The manuscript investigates the propagation of gravitational waves under isotropic Lorentz- and diffeomorphism-violating operators in the linearized gravitational sector of the Standard Model Extension. It focuses on the combined effects of the CPT-even dimension-four coefficient k^(4)_(I) and the CPT-odd dimension-five coefficient k^(5)_(V), deriving a modified dispersion relation that rescales propagation speed and introduces helicity-dependent corrections. This leads to birefringence and polarization mixing without additional propagating degrees of freedom. The authors construct the associated retarded Green function, obtain explicit waveform expressions for matter sources, apply the framework to a binary black hole system, and translate existing constraints from GW170817/GRB 170817A and GWTC-3 into bounds on the coefficients.

Significance. If the central claims are verified, particularly the mode content and absence of instabilities, the work supplies explicit, usable expressions for Lorentz-violating corrections to gravitational waveforms and the retarded propagator. These can be directly compared with existing and future detector data, extending prior SME analyses by treating the isotropic combination of dimension-four and dimension-five operators in a unified propagation calculation.

major comments (1)
  1. [Section deriving the modified wave operator and dispersion relation] The central claim that the modified wave operator produces only the two tensor modes (with birefringence but no extra propagating degrees of freedom) is load-bearing for the Green-function construction and all subsequent waveform results. For the CPT-odd dimension-five term, which introduces a third-order derivative piece, the manuscript must supply an explicit characteristic analysis of the isotropic wave operator (including the combined k^(4)_(I) + k^(5)_(V) contribution) and demonstrate that the characteristic polynomial factors into exactly two physical roots while any additional root is either non-propagating or identically zero.
minor comments (2)
  1. [Green function derivation] Clarify the precise definition of the isotropic projections for both operators and confirm that all higher-order terms are retained consistently when constructing the retarded Green function.
  2. [Application to binary systems] In the binary-black-hole application, state explicitly which post-Newtonian order is used for the quadrupole formula before applying the Lorentz-violating corrections.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The single major comment raises a valid point about the need for an explicit characteristic analysis to confirm the mode content. We address it below and will revise the manuscript to incorporate the requested analysis.

read point-by-point responses

  1. Referee: [Section deriving the modified wave operator and dispersion relation] The central claim that the modified wave operator produces only the two tensor modes (with birefringence but no extra propagating degrees of freedom) is load-bearing for the Green-function construction and all subsequent waveform results. For the CPT-odd dimension-five term, which introduces a third-order derivative piece, the manuscript must supply an explicit characteristic analysis of the isotropic wave operator (including the combined k^(4)_(I) + k^(5)_(V) contribution) and demonstrate that the characteristic polynomial factors into exactly two physical roots while any additional root is either non-propagating or identically zero.

    Authors: We agree that an explicit characteristic analysis strengthens the central claim and is necessary for rigor, particularly given the third-order term. In the revised manuscript we will add a dedicated subsection performing this analysis for the combined isotropic operator. We will derive the principal symbol of the wave operator in Fourier space, form the characteristic polynomial, and show that it factors into precisely two physical roots (corresponding to the right- and left-circularly polarized tensor modes with the modified dispersion relation). The additional root is identically zero, arising from the structure of the isotropic coefficients together with the transverse-traceless gauge constraints that eliminate scalar and vector modes. This confirms the absence of extra propagating degrees of freedom while preserving the birefringence and polarization-mixing effects already derived. The Green function and waveform expressions remain unchanged but will be cross-referenced to the new analysis. revision: yes

Circularity Check

0 steps flagged

Minor self-citation to SME framework; central derivation of modified dispersion, Green function, and waveform corrections remains independent

full rationale

The paper starts from the standard linearized SME wave operator for isotropic k^(4)_(I) and k^(5)_(V), derives the modified dispersion relation, constructs the retarded Green function, and obtains explicit quadrupole waveform corrections with shifted retarded times and amplitude rescaling. These steps are performed directly from the modified operator without reducing to a fitted parameter or self-referential definition. Bounds on the coefficients are obtained by reinterpreting published external constraints (GW170817/GRB 170817A and GWTC-3 propagation tests) under conservative polarization arguments rather than by fitting new data to the model. Any self-citation to prior SME literature is expected for the operator definitions but is not load-bearing for the propagation or Green-function results. No self-definitional, fitted-input, uniqueness-imported, or ansatz-smuggled circularity is exhibited by the paper's own equations.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on the validity of the linearized gravitational sector of the SME, the restriction to isotropic operators, and the direct applicability of existing multi-messenger constraints without additional modeling of anisotropic or higher-order effects.

free parameters (2)
  • k^(4)_(I)
    CPT-even dimension-four isotropic coefficient whose value is constrained rather than derived from first principles in this work.
  • k^(5)_(V)
    CPT-odd dimension-five isotropic coefficient whose value is constrained rather than derived from first principles in this work.
axioms (2)
  • domain assumption Linearized gravitational sector of the Standard Model Extension with only isotropic contributions from the specified operators.
    Invoked to simplify the dispersion relation and wave operator analysis.
  • domain assumption Existing GW170817 and GWTC-3 constraints can be mapped directly onto the chosen SME coefficients via polarization consistency arguments.
    Used to obtain the final bounds on the violation parameters.

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Reference graph

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