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arxiv: 2604.21990 · v1 · submitted 2026-04-23 · 🌀 gr-qc · hep-th

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A New Spin on Dissipative Tides: First-Post-Newtonian Effects in Compact Binary Inspirals

Anand Balivada , Abhishek Hegade K. R. , Nicol\'as Yunes
Authors on Pith no claims yet

Pith reviewed 2026-05-09 20:48 UTC · model grok-4.3

classification 🌀 gr-qc hep-th
keywords tidal dissipationpost-Newtoniangravitational wavescompact binariesspin effectsbinary inspiralswaveform modelingenergy balance
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0 comments X

The pith

Spin-induced tidal dissipation enters the gravitational-wave phase at 2.5 post-Newtonian order with a logarithmic frequency dependence.

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

The paper derives the first post-Newtonian corrections to the motion and energy balance of spinning compact binaries that arise from dissipative electric-quadrupolar tides. Using the most general linear tidal response allowed by rotational symmetry at low frequencies, it obtains the Fourier-domain gravitational-wave phase correction for quasi-circular, aligned-spin orbits. The resulting term appears at 2.5 post-Newtonian order and contains an explicit logarithm of frequency, which prevents it from being absorbed into the usual coalescence-time parameter. The calculation recovers known horizon absorption for extreme-mass-ratio black-hole binaries and flags a possible redshift correction missing from some comparable-mass worldline calculations.

Core claim

Spin-induced tidal dissipation enters the gravitational-wave phase at 2.5 post-Newtonian order and carries a logarithmic frequency dependence, so it is not degenerate with the coalescence phase. For binary black holes the dissipative flux reproduces horizon absorption in the extreme-mass-ratio limit and indicates a redshift-related correction in the comparable-mass case.

What carries the argument

The generalized energy-balance law that incorporates the first-post-Newtonian dissipative tidal flux for quasi-circular, aligned-spin orbits, which directly supplies the logarithmic phase correction.

If this is right

  • Dissipative spin-tide effects must be included at 2.5PN order in waveform models for high signal-to-noise detections.
  • The logarithmic frequency dependence distinguishes the effect from standard coalescence-phase parameters.
  • The derived flux matches horizon absorption for extreme-mass-ratio black-hole binaries.
  • A redshift-related correction appears for comparable-mass black-hole binaries that may be absent from existing worldline calculations.

Where Pith is reading between the lines

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

  • Waveform templates used for parameter estimation in LIGO-Virgo-KAGRA data may need this term to avoid systematic bias in spin and tidal measurements.
  • The noted discrepancy with certain worldline effective-field-theory results could be resolved by including the redshift factor explicitly in those frameworks.
  • The same formalism can be extended to misaligned spins or higher multipoles once the appropriate tidal response functions are known.

Load-bearing premise

The most general low-frequency linear tidal response compatible with rotational symmetry is sufficient to capture the dissipative effects.

What would settle it

Numerical-relativity waveforms for spinning binary black holes or extreme-mass-ratio inspirals that can be compared directly to the predicted 2.5PN logarithmic phase term.

Figures

Figures reproduced from arXiv: 2604.21990 by Abhishek Hegade K. R., Anand Balivada, Nicol\'as Yunes.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Cartoon (not to scale) depicting the motion of two [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
read the original abstract

Tidal dissipation in spinning compact binaries imprints characteristic corrections on the late-inspiral gravitational-wave signal. We develop a next-to-leading order post-Newtonian description of dissipative, electric-quadrupolar tides in spinning compact binaries, deriving the center-of-mass equations of motion, a generalized energy-balance law, and the corresponding Fourier-phase correction for quasi-circular orbits with spins aligned or anti-aligned with the orbital angular momentum. Using the most general, low-frequency, linear tidal response compatible with rotational symmetry, we show that spin-induced tidal dissipation enters the gravitational-wave phase at 2.5 post-Newtonian order and carries a logarithmic frequency dependence, so it is not degenerate with the coalescence phase. For binary black holes, our dissipative flux reproduces horizon absorption in the extreme-mass-ratio limit and points to a redshift-related correction in the comparable-mass case potentially not included in certain recent worldline effective field theory calculations. These results provide new waveform ingredients for precision modeling of spinning compact binaries in the high-signal-to-noise era.

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 develops a next-to-leading-order post-Newtonian description of dissipative electric-quadrupolar tides in spinning compact binaries. It derives the center-of-mass equations of motion, a generalized energy-balance law, and the Fourier-phase correction for quasi-circular orbits with aligned or anti-aligned spins. Using the most general low-frequency linear tidal response compatible with rotational symmetry, the work shows that spin-induced tidal dissipation enters the gravitational-wave phase at 2.5PN order with a logarithmic frequency dependence, rendering it non-degenerate with the coalescence phase. For black-hole binaries the dissipative flux recovers horizon absorption in the extreme-mass-ratio limit and identifies a redshift-related correction for the comparable-mass case that may be absent from some recent worldline EFT calculations.

Significance. If the derivations are correct, the result supplies concrete new waveform ingredients for precision modeling of spinning compact binaries. The distinct 2.5PN logarithmic term offers a potentially measurable signature that is not absorbed into the coalescence phase, which is valuable for high-SNR events. The explicit match to the known EMR horizon-absorption result and the identification of a possible missing redshift term in EFT calculations are strengths that could guide future comparisons between PN, EFT, and numerical-relativity approaches.

major comments (1)
  1. The claim that the dissipative flux points to a redshift-related correction in the comparable-mass case (abstract and concluding discussion) is load-bearing for the paper's broader implications. An explicit term-by-term comparison with the referenced worldline EFT calculations, including the precise coefficient or term that is absent, is needed to substantiate the statement.
minor comments (2)
  1. The title refers to 'First-Post-Newtonian Effects' while the abstract states that dissipation enters the phase at 2.5PN order; a brief clarifying sentence on the PN counting (tidal response at 1PN versus phase at 2.5PN) would avoid potential confusion.
  2. The abstract states that the most general linear low-frequency tidal response is adopted, but the manuscript should explicitly note (e.g., in the methods section) that this choice excludes nonlinear or finite-frequency corrections by construction and that such corrections are assumed to enter only at higher PN orders for the systems considered.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the positive assessment of its potential impact on waveform modeling. We address the single major comment below and will revise the manuscript accordingly to strengthen the relevant claim.

read point-by-point responses

  1. Referee: The claim that the dissipative flux points to a redshift-related correction in the comparable-mass case (abstract and concluding discussion) is load-bearing for the paper's broader implications. An explicit term-by-term comparison with the referenced worldline EFT calculations, including the precise coefficient or term that is absent, is needed to substantiate the statement.

    Authors: We agree that the claim would be more robust with an explicit comparison. In the revised manuscript we will add a new subsection (or appendix) that performs a term-by-term comparison of our post-Newtonian dissipative flux against the worldline EFT results cited in the paper. This comparison will (i) confirm exact agreement with the known horizon-absorption result in the extreme-mass-ratio limit and (ii) isolate the redshift-related factor that is present in our derivation but appears to be missing from the EFT expressions for comparable-mass binaries. We will also update the abstract and concluding discussion to reference this new comparison. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained from general assumptions and standard methods

full rationale

The paper derives the 2.5PN dissipative tidal phase correction starting from the most general low-frequency linear tidal response compatible with rotational symmetry, combined with standard post-Newtonian expansions for the equations of motion and energy balance. This produces the logarithmic frequency dependence as a direct consequence of the response function's structure without any reduction to fitted inputs or self-referential definitions. The reproduction of known horizon absorption in the extreme-mass-ratio limit functions as an external consistency check rather than a load-bearing input. No self-citation chains, ansatz smuggling, or renaming of known results are indicated in the provided abstract or reader's summary as central to the derivation. The central claim remains independent of the paper's own prior outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Relies on standard post-Newtonian expansion and linear tidal response assumptions from prior literature; no new free parameters or invented entities are introduced in the abstract.

axioms (2)
  • domain assumption Post-Newtonian expansion remains valid for velocities and separations in the late inspiral of compact binaries
    Standard assumption invoked for deriving equations of motion and phase corrections.
  • domain assumption Tidal response is linear, low-frequency, and compatible with rotational symmetry
    Used to model dissipative electric-quadrupolar tides without higher-order or nonlinear effects.

pith-pipeline@v0.9.0 · 5489 in / 1374 out tokens · 38524 ms · 2026-05-09T20:48:20.522979+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

81 extracted references · 41 canonical work pages · 2 internal anchors

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    Love numbers

    ˙rn<avb> + 3 c2r4 " −2ϵ def nd (δab −5n ab)S e 1 vf −3ϵ de (anb) Sd 1 ve +ϵ de (avb)ndSe 1 −5 ˙rϵde (anb)dSe 1 # +O c−3 .(10) The mass and spin evolution equations for body 1 can be obtained by acting on Eqs. (9a) and (9b) with the label exchange operator. D. Tidal Response The dynamical equations of motion, consisting of Eqs. (1), (9a) and (9b), are not ...

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    +v 2 ˙r2(76−108X 1 −5X 2 1)− M(2 + 22X1 +X 2 1) 2r + 1↔2.(40) We note that HRY denote the dissipative tidal deformability of bodyAasΞA instead ofH (0) A . IV. GRAVITATIONAL-WAVE PHASE FOR A QUASI-CIRCULAR ORBIT In this section, we compute the phase of the gravitational-waves emitted by the binary, assuming a quasi-circular orbit. The organization is as fo...

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    +O(x 3/2) −Λ (1) 2 χ2( ˆS2 i ˆLi)X5 2 x13/2 6(−5 + 3X2) + 1 56 x(−709 + 13544X2 −19565X 2 2 + 7434X3

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    +O(x 3/2) + Λ(2) 2 χ2 2X4 2 x5 2X1 − 5 56 x(−45 + 164X2 −273X 2 2 + 154X3

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    +O(x 3/2) + Λ(4) 2 χ4 2X4 2 x5 2X1 − 5 56 x(−45 + 164X2 −273X 2 2 + 154X3

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    +O(x 3/2) + (1)↔(2) ) ,(53) where the point-particle gravitational-wave flux on a quasi-circular orbit,⟨FGW⟩pp, is a result known up to4.5PN[7]. The adiabatic non-spinning tidal contribution, i.e., theΛ(0) 2 terms, are known all the way up to2PN order and beyond for non-spinning binaries [46, 50], with the1PN result having been computed in [43] using the ...

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    TheΛ (0) 2 term was also derived in [43], but differs from ours at 1PN, due to the differences of convention described in Sec

    +O(x 3/2) i + 3 2Λ(1) 2 ( ˆS2 i ˆLi)χ2x13/2X1X5 2 h 12 +x 19−4X 2 + 27X2 2 +O(x 3/2) i +1 6Λ(2) 2 χ2 2x5X1X4 2 h 9 + 7x 6 + 3X2 + 2X2 2 +O(x 3/2) i +1 6Λ(4) 2 χ4 2x5X1X4 2 h 9 + 7x 6 + 3X2 + 2X2 2 +O(x 3/2) i + 1↔2 , (55) where⟨E orb⟩pp is a known result for point particles [7]. TheΛ (0) 2 term was also derived in [43], but differs from ours at 1PN, due t...

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    (63) With the mass-absorption rate computed in [23], one can write the orbital-energy balance as ˙Eorb,EFT =F GW +⟨F Tdiss⟩EFT ,(64) where⟨F Tdiss⟩EFT =−dM/dt| EFT

    +O(x 3/2) i + 1↔2. (63) With the mass-absorption rate computed in [23], one can write the orbital-energy balance as ˙Eorb,EFT =F GW +⟨F Tdiss⟩EFT ,(64) where⟨F Tdiss⟩EFT =−dM/dt| EFT. We now compare this worldline EFT tidal dissipative flux with our comparable-mass expressions. Using the ex- pressions for the Love numbers from Eq. (3.35) and (3.36) of [23...

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    The termFTdiss,rem 17 from Eq

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