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arxiv: 2603.28689 · v2 · submitted 2026-03-30 · 🌀 gr-qc · astro-ph.HE· hep-ph

Recognition: 2 theorem links

· Lean Theorem

Probing soft signals of gravitational-wave memory with space-based interferometers

Yan Cao , Yong-Liang Ma , Yong Tang
Authors on Pith no claims yet

Pith reviewed 2026-05-14 01:54 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.HEhep-ph
keywords gravitational wave memorydisplacement memoryspace-based interferometersLISAsoft gravitonsblack hole mergerscompact binary scatteringstochastic background
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The pith

A single LISA-like detector can independently measure soft gravitational-wave displacement memory signals at signal-to-noise ratios of 10 or higher.

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

This paper shows how the low-frequency spectra of gravitational waves from moderately relativistic compact binary scatterings and nearly equal-mass black hole mergers match the shape of a corrected soft displacement-memory waveform. These simple spectral forms act as templates for matched filtering, allowing space-based interferometers to isolate the permanent spacetime offset left after such events. Simulations of Bayesian parameter estimation indicate that one LISA-like detector suffices for an independent measurement once the signal-to-noise ratio reaches about 10, while networks such as LISA-Taiji sharpen the constraints. The same approach also opens detection of null memory from stellar-mass mergers with a BBO-class instrument and assessment of a stochastic background composed of many such memory bursts.

Core claim

The low-frequency spectrum of gravitational waves from moderately relativistic compact binary scattering and nearly equal-mass quasi-circular non-precessing black hole mergers can be described by a corrected soft waveform of displacement memory. This description enables independent measurement of the soft displacement-memory signal with a single LISA-like detector at signal-to-noise ratios ≳ 10, with joint LISA-Taiji observations improving precision. A single BBO detector can separately measure null memory from stellar-mass compact binary mergers, and an idealized stochastic background of soft displacement-memory signals remains detectable.

What carries the argument

The corrected soft waveform of displacement memory, which supplies a universal low-frequency template for matched filtering and parameter estimation of gravitational-wave signals.

If this is right

  • Independent measurement of a soft displacement-memory signal is achievable with a single LISA-like detector at signal-to-noise ratios ≳ 10.
  • Joint observations with a LISA-Taiji network significantly improve the precision of the memory measurement.
  • A single BBO detector can separately measure the null memory component from stellar-mass compact binary mergers.
  • An idealized stochastic background of soft displacement-memory signals can be evaluated for detectability with space-based interferometers.

Where Pith is reading between the lines

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

  • Detection of these soft signals would give access to the infrared limit of gravitational radiation that oscillatory components alone do not reveal at low frequencies.
  • The template approach could be extended to velocity-memory and integrated-displacement-memory waveforms to search for additional low-frequency features in the same data sets.
  • Networked observations would help separate memory contributions from instrumental noise and astrophysical foregrounds in realistic observing runs.

Load-bearing premise

The low-frequency spectrum of the examined compact binary scattering and black hole merger events can be described by a corrected soft waveform of displacement memory.

What would settle it

A direct comparison showing that the actual low-frequency spectrum from a moderately relativistic compact binary scattering event deviates substantially from the shape predicted by the corrected soft displacement-memory waveform.

Figures

Figures reproduced from arXiv: 2603.28689 by Yan Cao, Yong-Liang Ma, Yong Tang.

Figure 2
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read the original abstract

Gravitational-wave displacement memory is a remarkable and ubiquitous phenomenon predicted by general relativity, which has not yet been detected. Unlike the oscillatory components of gravitational waveforms, displacement memory is associated with soft gravitons, making it the only observable signal of its parent event at sufficiently low frequencies. Similarly, soft waveforms may arise from velocity and integrated-displacement memory. The simple and universal spectral shapes of soft waveforms also provide effective templates for matched filtering and parameter estimation. In this paper, we investigate the detection prospects for such soft memory signals with future space-based laser interferometers. As realistic examples, we examine the infrared spectral features of gravitational waves from moderately relativistic compact binary scattering and nearly equal-mass quasi-circular, non-precessing black hole mergers. In both cases, the low frequency spectrum can be described by a corrected soft waveform of displacement memory. The results of simulated Bayesian parameter estimation demonstrate that independent measurement of a soft displacement-memory signal with a single LISA-like detector is achievable at signal-to-noise ratios $\gtrsim 10$. The measurement precision can be significantly improved by joint observations with a LISA-Taiji network. A single BBO detector could be capable of separately measuring the null memory from stellar-mass compact binary mergers. We also evaluate the detectability of an idealized stochastic background of soft displacement-memory signals. Our results indicate that gravitational-wave bursts with memory can be promising targets for space-based interferometers.

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 / 0 minor

Summary. The paper claims that soft displacement-memory signals from gravitational waves can be independently measured with a single LISA-like space-based interferometer at signal-to-noise ratios ≳10, based on the low-frequency spectra of moderately relativistic compact binary scattering and nearly equal-mass quasi-circular non-precessing black hole mergers being accurately captured by a corrected soft waveform of displacement memory. Simulated Bayesian parameter estimation supports this threshold, with improved precision from LISA-Taiji networks, and the work also assesses detectability of an idealized stochastic background of such signals.

Significance. If the waveform modeling and recovery results hold, this would be a significant contribution by providing concrete detection prospects for the soft sector of gravitational waves and memory effects with future space-based detectors, using universal spectral templates that simplify matched filtering and parameter estimation. The focus on infrared features and network synergies offers a practical path toward observing GR predictions that remain undetected.

major comments (1)
  1. [Abstract and sections on infrared spectral features of the examined events] The central claim that independent measurement at SNR ≳10 is achievable rests on the assertion (in the abstract and the sections examining the two source classes) that the low-frequency spectrum is accurately described by a corrected soft waveform of displacement memory. However, no quantitative bounds are given on the size of the correction, the frequency range of validity, or the residual mismatch with the true waveform (including finite-velocity effects, nonlinear memory, or higher multipoles). Without explicit validation or mismatch metrics for these source classes, the Bayesian recovery results and detection thresholds cannot be reliably assessed.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive major comment. We appreciate the positive assessment of the work's potential significance. We address the concern below and will incorporate the requested validation into the revised manuscript.

read point-by-point responses

  1. Referee: The central claim that independent measurement at SNR ≳10 is achievable rests on the assertion (in the abstract and the sections examining the two source classes) that the low-frequency spectrum is accurately described by a corrected soft waveform of displacement memory. However, no quantitative bounds are given on the size of the correction, the frequency range of validity, or the residual mismatch with the true waveform (including finite-velocity effects, nonlinear memory, or higher multipoles). Without explicit validation or mismatch metrics for these source classes, the Bayesian recovery results and detection thresholds cannot be reliably assessed.

    Authors: We agree that explicit quantitative validation is required to support the central claims. The manuscript asserts that the infrared spectra of the two source classes are captured by the corrected soft displacement-memory waveform on the basis of the soft-graviton theorem and the specific kinematics (moderately relativistic scattering and quasi-circular non-precessing mergers), but we did not supply mismatch metrics or bounds on residual corrections. In the revised manuscript we will add a dedicated subsection (and associated figures) that computes the overlap and residual mismatch between the full waveforms and the soft template in the LISA band (∼10^{-4}–10^{-2} Hz). We will quantify the size of finite-velocity corrections, nonlinear-memory contributions, and higher-multipole effects, and we will state the frequency range over which the approximation holds to within a few percent. These additions will directly substantiate the reported SNR ≳10 threshold and the Bayesian recovery results. revision: yes

Circularity Check

0 steps flagged

No circularity: soft-waveform template adopted from external GR literature

full rationale

The paper applies a corrected soft displacement-memory waveform template taken from prior general-relativity literature to generate detector-response templates for Bayesian parameter estimation on two source classes. No equation reduces by construction to a fitted parameter, no self-citation chain supplies the central premise, and the low-frequency spectral description is presented as an input assumption rather than a derived output. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The analysis rests on the standard GR prediction of displacement memory and the validity of the soft-graviton approximation at low frequencies; no new free parameters or entities are introduced in the abstract.

axioms (1)
  • domain assumption General relativity predicts a permanent displacement memory effect in gravitational waves
    Invoked as the starting point for all soft-signal modeling.

pith-pipeline@v0.9.0 · 5554 in / 1085 out tokens · 45384 ms · 2026-05-14T01:54:56.708135+00:00 · methodology

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Works this paper leans on

102 extracted references · 102 canonical work pages · 3 internal anchors

  1. [1]

    V. B. Braginsky and K. S. Thorne, Nature 327, 123 (1987)

    work page 1987

  2. [2]

    Christodoulou, Phys

    D. Christodoulou, Phys. Rev. Lett. 67, 1486 (1991)

    work page 1991

  3. [3]

    K. S. Thorne, Phys. Rev. D 45, 520 (1992)

    work page 1992

  4. [4]

    Favata, Classical and Quantum Gravity 27, 084036 (2010)

    M. Favata, Classical and Quantum Gravity 27, 084036 (2010)

    work page 2010

  5. [5]

    Bieri and D

    L. Bieri and D. Garfinkle, Physical Review D 89, 10.1103/physrevd.89.084039 (2014)

    work page doi:10.1103/physrevd.89.084039 2014

  6. [6]

    Winicour, Classical and Quantum Gravity 31, 205003 (2014)

    J. Winicour, Classical and Quantum Gravity 31, 205003 (2014)

    work page 2014

  7. [7]

    É. É. Flanagan and D. A. Nichols, Phys. Rev. D 92, 084057 (2015) , [Erratum: Phys.Rev.D 93, 049905 (2016)], arXiv:1411.4599 [gr-qc]

    work page arXiv 2015

  8. [8]

    Strominger and A

    A. Strominger and A. Zhiboedov, Gravitational mem- ory, bms supertranslations and soft theorems (2014), arXiv:1411.5745 [hep-th]

    work page arXiv 2014

  9. [9]

    Mitman et al., Physical Review D 102, 10.1103/physrevd.102.104007 (2020)

    K. Mitman et al., Physical Review D 102, 10.1103/physrevd.102.104007 (2020)

    work page doi:10.1103/physrevd.102.104007 2020

  10. [11]

    Favata, Astrophysical Journal 696, L159 (2009)

    M. Favata, Astrophysical Journal 696, L159 (2009)

    work page 2009

  11. [13]

    Talbot, E

    C. Talbot, E. Thrane, P. D. Lasky, and F. Lin, Phys. Rev. D 98, 064031 (2018)

    work page 2018

  12. [14]

    Yang and D

    H. Yang and D. Martynov, Physical Review Letters 121, 10.1103/physrevlett.121.071102 (2018)

    work page doi:10.1103/physrevlett.121.071102 2018

  13. [15]

    Ebersold, Y

    M. Ebersold, Y. Boetzel, G. Faye, C. K. Mishra, B. R. Iyer, and P. Jetzer, Physical Review D 100, 10.1103/physrevd.100.084043 (2019)

    work page doi:10.1103/physrevd.100.084043 2019

  14. [16]

    Tiwari, M

    S. Tiwari, M. Ebersold, and E. Z. Hamilton, Physical Review D 104, 10.1103/physrevd.104.123024 (2021)

    work page doi:10.1103/physrevd.104.123024 2021

  15. [17]

    X. Liu, X. He, and Z. Cao, Physical Review D 103, 10.1103/physrevd.103.043005 (2021)

    work page doi:10.1103/physrevd.103.043005 2021

  16. [18]

    Z.-C. Zhao, X. Liu, Z. Cao, and X. He, Physical Review D 104, 10.1103/physrevd.104.064056 (2021)

    work page doi:10.1103/physrevd.104.064056 2021

  17. [19]

    Islam, S

    T. Islam, S. E. Field, G. Khanna, and N. Warburton, Physical Review D 108, 10.1103/physrevd.108.024046 (2023)

    work page doi:10.1103/physrevd.108.024046 2023

  18. [20]

    Henry and M

    Q. Henry and M. Khalil, Phys. Rev. D 108, 104016 (2023)

    work page 2023

  19. [22]

    Dandapat et al., Physical Review D 108, 10.1103/physrevd.108.024013 (2023)

    S. Dandapat et al., Physical Review D 108, 10.1103/physrevd.108.024013 (2023)

    work page doi:10.1103/physrevd.108.024013 2023

  20. [23]

    A. Hait, S. Mohanty, and S. Prakash, Physical Review D 109, 10.1103/physrevd.109.084037 (2024)

    work page doi:10.1103/physrevd.109.084037 2024

  21. [24]

    Lopez, S

    D. Lopez, S. Tiwari, and M. Ebersold, Physical Review D 109, 10.1103/physrevd.109.043039 (2024)

    work page doi:10.1103/physrevd.109.043039 2024

  22. [25]

    Gasparotto, G

    S. Gasparotto, G. Franciolini, and V. Domcke, Phys. Rev. D 112, 103021 (2025)

    work page 2025

  23. [26]

    Hou, Z.-C

    S. Hou, Z.-C. Zhao, Z. Cao, and Z.-H. Zhu, Chin. Phys. Lett. 42, 101101 (2025)

    work page 2025

  24. [27]

    Elhashash and D

    A. Elhashash and D. A. Nichols, Physical Review D 111, 10.1103/physrevd.111.044052 (2025)

    work page doi:10.1103/physrevd.111.044052 2025

  25. [28]

    Cunningham et al., Classical and Quantum Gravity 42, 135009 (2025)

    K. Cunningham et al., Classical and Quantum Gravity 42, 135009 (2025)

    work page 2025

  26. [29]

    Bamber, A

    J. Bamber, A. Tsokaros, M. Ruiz, S. L. Shapiro, M. Fa- vata, M. Karlson, and F. V. Piñas, The gravitational wave memory from binary neutron star mergers (2025), arXiv:2510.09742 [gr-qc]

    work page arXiv 2025

  27. [30]

    N. Sago, K. Ioka, T. Nakamura, and R. Yamazaki, Phys- ical Review D 70, 10.1103/physrevd.70.104012 (2004)

    work page doi:10.1103/physrevd.70.104012 2004

  28. [31]

    Sakai et al., Physical Review D 112, 10.1103/58pt- ms85 (2025)

    Y. Sakai et al., Physical Review D 112, 10.1103/58pt- ms85 (2025)

    work page doi:10.1103/58pt- 2025

  29. [32]

    Mukhopadhyay, C

    M. Mukhopadhyay, C. Cardona, and C. Lunardini, Journal of Cosmology and Astroparticle Physics 2021 (07), 055

    work page 2021

  30. [33]

    C. J. Richardson et al., Physical Review D 105, 10.1103/physrevd.105.103008 (2022)

    work page doi:10.1103/physrevd.105.103008 2022

  31. [35]

    L. O. McNeill, E. Thrane, and P. D. Lasky, Phys. Rev. Lett. 118, 181103 (2017) , arXiv:1702.01759 [astro- ph.IM]

    work page arXiv 2017

  32. [36]

    Ebersold and S

    M. Ebersold and S. Tiwari, Physical Review D 101, 10.1103/physrevd.101.104041 (2020)

    work page doi:10.1103/physrevd.101.104041 2020

  33. [37]

    Hübner, C

    M. Hübner, C. Talbot, P. D. Lasky, and E. Thrane, Physical Review D 101, 10.1103/physrevd.101.023011 (2020)

    work page doi:10.1103/physrevd.101.023011 2020

  34. [38]

    Hübner, P

    M. Hübner, P. Lasky, and E. Thrane, Physical Review D 104, 10.1103/physrevd.104.023004 (2021)

    work page doi:10.1103/physrevd.104.023004 2021

  35. [39]

    A. M. Grant and D. A. Nichols, Physical Review D 107, 10.1103/physrevd.107.064056 (2023)

    work page doi:10.1103/physrevd.107.064056 2023

  36. [40]

    S. Y. Cheung, P. D. Lasky, and E. Thrane, Classical and Quantum Gravity 41, 115010 (2024)

    work page 2024

  37. [41]

    Goncharov, L

    B. Goncharov, L. Donnay, and J. Harms, Physical Review Letters 132, 10.1103/physrevlett.132.241401 (2024)

    work page doi:10.1103/physrevlett.132.241401 2024

  38. [42]

    K. Islo, J. Simon, S. Burke-Spolaor, and X. Siemens, Prospects for memory detection with low-frequency gravitational wave detectors (2019), arXiv:1906.11936 [astro-ph.HE]

    work page arXiv 2019

  39. [45]

    Inchauspé, S

    H. Inchauspé, S. Gasparotto, D. Blas, L. Heisenberg, J. Zosso, and S. Tiwari, Phys. Rev. D 111, 044044 (2025), arXiv:2406.09228 [gr-qc]

    work page arXiv 2025

  40. [46]

    S. Sun, C. Shi, J.-d. Zhang, and J. Mei, Phys. Rev. D 110, 024050 (2024) , arXiv:2401.11416 [gr-qc]

    work page arXiv 2024

  41. [47]

    Cogez et al., Detectability of gravitational-wave memory with lisa: A bayesian approach (2026), arXiv:2601.23230 [gr-qc]

    A. Cogez et al., Detectability of gravitational-wave memory with lisa: A bayesian approach (2026), arXiv:2601.23230 [gr-qc]

    work page arXiv 2026

  42. [48]

    Toward claiming a detection of gravitational memory

    J. Zosso, L. M. Zertuche, S. Gasparotto, A. Cogez, H. Inchauspé, and M. Jacobs, Towards claiming a detec- tion of gravitational memory (2026), arXiv:2601.23019 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  43. [49]

    van Haasteren and Y

    R. van Haasteren and Y. Levin, Monthly Notices of the Royal Astronomical Society 401, 2372–2378 (2010)

    work page 2010

  44. [50]

    J. B. Wang et al., Monthly Notices of the Royal Astro- nomical Society 446, 1657–1671 (2014)

    work page 2014

  45. [51]

    Aggarwal et al., The Astrophysical Journal 889, 38 (2020)

    K. Aggarwal et al., The Astrophysical Journal 889, 38 (2020)

    work page 2020

  46. [52]

    J. Sun, P. T. Baker, A. D. Johnson, D. R. Madison, and X. Siemens, The Astrophysical Journal 951, 121 (2023)

    work page 2023

  47. [53]

    Dandapat et al., Physical Review D 109, 10.1103/physrevd.109.103018 (2024)

    S. Dandapat et al., Physical Review D 109, 10.1103/physrevd.109.103018 (2024). 30

    work page doi:10.1103/physrevd.109.103018 2024

  48. [54]

    J. P. Sun, X. Siemens, and D. R. Madison, Phys. Rev. D 111, 102002 (2025)

    work page 2025

  49. [55]

    Agazie et al., The nanograv 15-year data set: Search for gravitational wave memory (2025), arXiv:2502.18599 [gr-qc]

    G. Agazie et al., The nanograv 15-year data set: Search for gravitational wave memory (2025), arXiv:2502.18599 [gr-qc]

    work page arXiv 2025

  50. [56]

    Zwick, D

    L. Zwick, D. O’Neill, K. Hendriks, P. Kirkeberg, and M. Miravet-Tenés, Astron. Astrophys. 694, A95 (2025) , arXiv:2404.06927 [astro-ph.CO]

    work page arXiv 2025

  51. [57]

    Fontbuté, T

    J. Fontbuté, T. Andrade, R. Luna, J. C. Bustillo, G. Morrás, S. Jaraba, J. García-Bellido, and G. L. Izquierdo, Phys. Rev. D 111, 044024 (2025)

    work page 2025

  52. [58]

    Cheng, Y

    Y.-Z. Cheng, Y. Cao, and Y. Tang, Phys. Rev. D 111, 083010 (2025) , arXiv:2411.03095 [gr-qc]

    work page arXiv 2025

  53. [59]

    R. K. Singh, S. Kumar, A. Chowdhuri, and A. Bhat- tacharyya, Gravitational memory meets astrophysical environments: exploring a new frontier through oscula- tions (2025), arXiv:2509.01676 [gr-qc]

    work page arXiv 2025

  54. [60]

    Alnasheet, V

    Q. Alnasheet, V. Cardoso, F. Duque, and R. P. Macedo, Phys. Rev. D 112, 044066 (2025)

    work page 2025

  55. [61]

    L. P. Grishchuk and A. G. Polnarev, Soviet Journal of Experimental and Theoretical Physics 69, 653 (1989)

    work page 1989

  56. [62]

    Bieri and A

    L. Bieri and A. Polnarev, Classical and Quantum Grav- ity 41, 135012 (2024)

    work page 2024

  57. [63]

    Laser Interferometer Space Antenna

    P. Amaro-Seoane et al., Laser interferometer space an- tenna (2017), arXiv:1702.00786 [astro-ph.IM]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  58. [64]

    Babak, M

    S. Babak, M. Hewitson, and A. Petiteau, Lisa sensitiv- ity and snr calculations (2021), arXiv:2108.01167 [astro- ph.IM]

    work page arXiv 2021

  59. [65]

    Hu and Y.-L

    W.-R. Hu and Y.-L. Wu, National Science Review 4, 685 (2017) , https://academic.oup.com/nsr/article- pdf/4/5/685/31566708/nwx116.pdf

    work page 2017

  60. [66]

    Corbin and N

    V. Corbin and N. J. Cornish, Classical and Quantum Gravity 23, 2435–2446 (2006)

    work page 2006

  61. [67]

    W.-H. Ruan, C. Liu, Z.-K. Guo, Y.-L. Wu, and R.-G. Cai, Nature Astronomy 4, 108–109 (2020)

    work page 2020

  62. [68]

    J. B. Achour and J.-P. Uzan, Journal of Cosmology and Astroparticle Physics 2024 (08), 004

    work page 2024

  63. [69]

    A. G. Wiseman and C. M. Will, Phys. Rev. D 44, R2945 (1991)

    work page 1991

  64. [70]

    Takahashi and T

    R. Takahashi and T. Nakamura, The Astrophysical Journal 595, 1039–1051 (2003)

    work page 2003

  65. [71]

    Bruyère and C

    E. Bruyère and C. Pitrou, Gravitational lensing beyond the eikonal approximation (2026), arXiv:2601.10239 [gr- qc]

    work page arXiv 2026

  66. [72]

    Weinberg, Phys

    S. Weinberg, Phys. Rev. 126, 1899 (1962)

    work page 1962

  67. [73]

    Bieri, D

    L. Bieri, D. Garfinkle, and N. Yunes, Classical and Quantum Gravity 34, 215002 (2017)

    work page 2017

  68. [74]

    García-Bellido and S

    J. García-Bellido and S. Nesseris, Physics of the Dark Universe 21, 61–69 (2018)

    work page 2018

  69. [75]

    L. E. Kidder, Phys. Rev. D 52, 821 (1995)

    work page 1995

  70. [76]

    Brax and D

    P. Brax and D. A. Steer, Phys. Rev. D 111, 104046 (2025), arXiv:2412.17938 [gr-qc]

    work page arXiv 2025

  71. [77]

    Damour and N

    T. Damour and N. Deruelle, Annales de L’Institut Henri Poincare Section (A) Physique Theorique 43, 107 (1985)

    work page 1985

  72. [78]

    Siemonsen, T

    N. Siemonsen, T. May, and W. E. East, Phys. Rev. D 107, 104003 (2023) , arXiv:2211.03845 [gr-qc]

    work page arXiv 2023

  73. [79]

    Cao, Y.-Z

    Y. Cao, Y.-Z. Cheng, G.-L. Li, and Y. Tang, Phys. Rev. D 111, 083011 (2025) , arXiv:2411.17247 [gr-qc]

    work page arXiv 2025

  74. [80]

    D. A. Nichols, Phys. Rev. D 95, 084048 (2017)

    work page 2017

  75. [81]

    Goryachev, W

    M. Goryachev, W. M. Campbell, I. S. Heng, S. Galliou, E. N. Ivanov, and M. E. Tobar, Phys. Rev. Lett. 127, 071102 (2021)

    work page 2021

  76. [82]

    M. M. Riva, F. Vernizzi, and L. K. Wong, Phys. Rev. D 108, 104052 (2023)

    work page 2023

  77. [83]

    Tinto and S

    M. Tinto and S. V. Dhurandhar, Living Rev. Rel. 8, 4 (2005), arXiv:gr-qc/0409034

    work page arXiv 2005

  78. [84]

    Hu, Gravitational wave astrophysics with tianqin: A brief progress review (2024), arXiv:2409.19664 [gr-qc]

    Y.-M. Hu, Gravitational wave astrophysics with tianqin: A brief progress review (2024), arXiv:2409.19664 [gr-qc]

    work page arXiv 2024

  79. [86]

    Krolak, M

    A. Krolak, M. Tinto, and M. Vallisneri, Phys. Rev. D 70, 022003 (2004) , [Erratum: Phys.Rev.D 76, 069901 (2007)], arXiv:gr-qc/0401108

    work page arXiv 2004

  80. [87]

    M. L. Katz, J.-B. Bayle, A. J. Chua, and M. Vallisneri, Physical Review D 106, 10.1103/physrevd.106.103001 (2022)

    work page doi:10.1103/physrevd.106.103001 2022

Showing first 80 references.