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arxiv: 2509.01614 · v2 · submitted 2025-09-01 · 🌀 gr-qc · astro-ph.HE

Probing modified gravitational-wave dispersion with bursts from eccentric black-hole binaries

Nicholas Loutrel , Ava Bailey , Davide Gerosa This is my paper

Pith reviewed 2026-05-18 19:32 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.HE
keywords gravitational wavesmodified gravitydispersion relationseccentric binariesLIGOFisher information matrixHořava-Lifschitz gravity
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0 comments X

The pith

Dispersion effects on bursts from eccentric black-hole binaries can yield bounds on some modified gravity models that are 1-3 orders of magnitude stronger than existing limits when observed by LIGO.

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

The paper studies how modified dispersion relations affect gravitational-wave bursts emitted by highly eccentric binary black holes. In these signals the dispersion alters the relative arrival times of successive bursts by a 2.5PN correction and introduces a Bessel-function amplitude modulation inside each burst. The authors apply the Fisher information matrix to forecast the precision with which future LIGO detections of repeating bursts could constrain the dispersion parameters in a range of modified-gravity scenarios. They find that the resulting limits depend strongly on the underlying theory: for Hořava-Lifschitz gravity and extra-dimension models the projected constraints improve substantially over current bounds, while for massive-graviton and multifractional-spacetime cases the constraints remain weaker.

Core claim

Within the low-energy effective-field-theory parameterization of modified dispersion, the waveform of an eccentric-binary burst acquires both a time-of-arrival shift between successive bursts and an internal harmonic amplitude modulation. Fisher-matrix projections on these features show that LIGO observations of repeating bursts can place bounds on the coupling constants of Hořava-Lifschitz gravity and extra-dimension scenarios that are one to three orders of magnitude tighter than present limits, while the same signals yield only weaker bounds for massive-graviton and multifractional models.

What carries the argument

Parameterized low-energy dispersion relation that produces a 2.5PN correction to inter-burst arrival-time differences together with a Bessel-type modulation of the orbital-harmonic amplitudes.

If this is right

  • Projected constraints on dispersion parameters are stronger for Lorentz-invariance-breaking models such as Hořava-Lifschitz gravity and extra dimensions than for massive-graviton or multifractional scenarios.
  • Repeating burst signals supply an independent channel for testing modified dispersion that is distinct from the usual inspiral-merger-ringdown analysis.
  • The dispersion-induced effects enter the waveform at 2.5PN order in the timing and through amplitude modulation of the harmonics.
  • Optimal LIGO observations of such bursts can improve existing bounds by 1-3 orders of magnitude for certain modified-gravity theories.

Where Pith is reading between the lines

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

  • The same burst signals might be cross-checked against standard quasi-circular inspirals to separate propagation effects from source-intrinsic modifications.
  • Higher-sensitivity detectors could extend the reach of these constraints to still weaker coupling values.
  • Non-detection of the predicted timing or amplitude signatures would directly rule out ranges of dispersion parameters in the favored models.

Load-bearing premise

The Fisher information matrix applied to the modified burst waveforms accurately captures the information content without significant bias from waveform systematics or noise non-stationarity.

What would settle it

A measured difference in arrival times or harmonic amplitudes in a repeating eccentric-binary burst signal that either matches or deviates from the specific 2.5PN shift and Bessel modulation predicted for a chosen dispersion parameter value.

Figures

Figures reproduced from arXiv: 2509.01614 by Ava Bailey, Davide Gerosa, Nicholas Loutrel.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: shows a comparison between the PN expansion of ga in Eq. (45) (dashed lines) and the exact expression in Eq. (44) (circles) for three different binary systems: a BBH (magenta), an NSBH (blue), and a BNS (red). Ta￾ble II shows the orbital parameters for each of the binary systems. The exact expression and PN result show ex￾cellent agreement, with the relative error (bottom panel) being ∼ O(10−5−10−3 ) after… view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Marginalized posterior distributions for the binary with [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Uncertainty on the parameter [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Violin plots on theory parameters found from taking the uncertainties on [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
read the original abstract

Gravitational waves in general relativity are non-dispersive, yet a host of modified theories predict dispersion effects during propagation. In this work, we consider the impact of dispersion effects on gravitational-wave bursts from highly eccentric binary black holes. We consider the dispersion effects within the low-energy, effective field theory limit, and model the dispersion relation via standard parameterized deformations. Such modified dispersion relations produce two modifications to the burst waveform: a modification to the time of arrival of the bursts in the detector, which appears as a 2.5PN correction to the difference in burst arrival times, and a modification to the arrival time of individual orbital harmonics within the bursts themselves, resulting in a Bessel-type amplitude modulation of the waveform. Using the Fisher information matrix, we study projected constraints one might obtain with future observations of repeating burst signals with LIGO. We find that the projected constraints vary significantly depending on the theoretical mechanism producing the modified dispersion. For massive gravitons and multifractional spacetimes that break Lorentz invariance, bounds on the coupling parameters are generally weaker than current bounds. For other Lorentz invariance breaking models such as Ho\v{r}ava-Lifschitz gravity, as well as scenarios with extra dimensions, the bounds in optimal cases can be 1-3 orders of magnitude stronger than current bounds.

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 claims that modified dispersion relations in gravity can be probed using gravitational-wave bursts from eccentric black-hole binaries. By modeling dispersion via standard parameterized deformations in the low-energy EFT limit, two effects are identified: a 2.5PN time-of-arrival shift between bursts and a Bessel-type amplitude modulation within bursts. Using the Fisher information matrix, projected constraints from future LIGO observations are derived, suggesting that for Hořava-Lifshitz gravity and extra-dimension models, bounds can be 1-3 orders of magnitude stronger than current ones in optimal cases.

Significance. If the results hold, this work demonstrates the utility of eccentric binary bursts for testing modified gravity, potentially offering tighter constraints on Lorentz-violating dispersion effects compared to existing methods. The distinction between different theoretical mechanisms leading to varying bound strengths is a notable contribution.

major comments (2)
  1. [Section on Fisher information matrix analysis] Section on Fisher information matrix analysis: The validity of the Fisher information matrix approximation for these low-SNR, burst-like signals is not demonstrated (e.g., via Monte Carlo injections or comparison to full likelihood sampling), which is critical since the projected constraints on the dispersion coupling parameters rest on this approximation.
  2. [Abstract and waveform modeling] Abstract and waveform modeling: The assumption that the standard parameterized dispersion relations accurately reproduce the waveform modifications for Hořava-Lifshitz gravity and extra-dimension scenarios may not hold due to possible higher-order terms (e.g., k^4) or anisotropies in those theories, which could introduce unaccounted degeneracies with eccentricity or sky position and invalidate the claimed 1-3 order improvements.
minor comments (2)
  1. The paper would benefit from a clearer discussion of the limitations of the low-energy EFT approximation when applied to specific modified gravity models.
  2. [Figure captions] Ensure that all figures clearly distinguish between the different dispersion models considered.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed comments, which have helped us clarify important aspects of our analysis. We address each major comment below and have revised the manuscript accordingly to strengthen the presentation of our results.

read point-by-point responses

  1. Referee: Section on Fisher information matrix analysis: The validity of the Fisher information matrix approximation for these low-SNR, burst-like signals is not demonstrated (e.g., via Monte Carlo injections or comparison to full likelihood sampling), which is critical since the projected constraints on the dispersion coupling parameters rest on this approximation.

    Authors: We agree that the Fisher matrix provides only an approximation to the true posterior, and its accuracy for low-SNR burst signals merits explicit discussion. In the revised manuscript we have added a dedicated paragraph in the Fisher analysis section that reviews the conditions under which the Fisher approximation remains useful for burst-like waveforms, cites relevant validation studies in the gravitational-wave literature, and explicitly states that the reported constraints should be viewed as indicative forecasts. A full Monte-Carlo injection study or comparison with nested sampling would provide a more rigorous validation but is computationally demanding and lies outside the scope of the present work, which centers on deriving the dispersion-induced waveform modifications and obtaining first-order projections. revision: partial

  2. Referee: Abstract and waveform modeling: The assumption that the standard parameterized dispersion relations accurately reproduce the waveform modifications for Hořava-Lifshitz gravity and extra-dimension scenarios may not hold due to possible higher-order terms (e.g., k^4) or anisotropies in those theories, which could introduce unaccounted degeneracies with eccentricity or sky position and invalidate the claimed 1-3 order improvements.

    Authors: The manuscript works strictly within the low-energy effective-field-theory limit, where the leading dispersion correction is captured by the standard parameterized form we adopt. For the Hořava-Lifshitz and extra-dimension models considered, this leading term dominates at LIGO frequencies. We have revised both the abstract and the waveform-modeling section to state explicitly that higher-order terms (such as k^4) and possible anisotropies are neglected in the present approximation. The Fisher matrix already marginalizes over eccentricity and sky-position parameters, thereby incorporating the leading degeneracies with those quantities. Our quoted improvements therefore apply to the effective dispersion model under the stated assumptions rather than to the complete ultraviolet completions of the theories. revision: yes

Circularity Check

0 steps flagged

No circularity: forward projections via standard Fisher analysis on parameterized EFT deformations

full rationale

The paper derives projected bounds on dispersion parameters by applying the Fisher information matrix to modeled burst waveforms from eccentric binaries. The two waveform modifications (2.5PN inter-burst timing shift and Bessel intra-burst modulation) follow directly from the chosen low-energy parameterized dispersion relation, which is adopted as standard input rather than fitted or derived within the paper. No equation reduces a claimed bound to a quantity already determined by the paper's own data or ansatz; results are explicit forward projections onto future LIGO observations, not retrofits. Self-citations, if present, are not load-bearing for the central mapping or covariance calculation. The derivation remains self-contained against the external Fisher formalism and EFT parameterization conventions.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The analysis rests on the low-energy EFT parameterization of the dispersion relation and the validity of the Fisher-matrix approximation for burst signals; no new particles or forces are introduced.

free parameters (1)
  • dispersion coupling parameter
    Each modified-gravity model introduces at least one free coupling constant whose value is to be constrained; these are the quantities whose bounds are reported.
axioms (2)
  • domain assumption Dispersion relation can be modeled by standard parameterized deformations in the low-energy effective-field-theory limit
    Invoked to derive both the time-of-arrival shift and the harmonic modulation inside each burst.
  • domain assumption Fisher information matrix provides a reliable estimate of parameter uncertainties for the simulated burst signals
    Used to obtain all projected constraints.

pith-pipeline@v0.9.0 · 5764 in / 1392 out tokens · 44635 ms · 2026-05-18T19:32:29.732537+00:00 · methodology

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Reference graph

Works this paper leans on

99 extracted references · 99 canonical work pages · 42 internal anchors

  1. [1]

    Tests of General Relativity with GWTC-3

    R. Abbottet al., (2021), arXiv:2112.06861 [gr-qc]. [2] T. Baker, E. Bellini, P. G. Ferreira, M. Lagos, J. Noller, 17 and I. Sawicki, Phys. Rev. Lett.119, 251301 (2017), arXiv:1710.06394 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  2. [2]

    B. P. Abbottet al.(LIGO Scientific, Virgo), Phys. Rev. Lett. 123, 011102 (2019), arXiv:1811.00364 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  3. [3]

    Ashtekar, A

    A. Ashtekar, A. del Río, and M. Schneider, Gen. Relat. Gravit. 54, 45 (2022), arXiv:2205.00298 [gr-qc]

    work page arXiv 2022

  4. [4]

    Carlip, Rep

    S. Carlip, Rep. Prog. Phys.64, 885 (2001), arXiv:gr- qc/0108040

    work page arXiv 2001

  5. [5]

    Scales and hierachies in asymptotically safe quantum gravity: a review

    G. Gubitosi, C. Ripken, and F. Saueressig, Found. Phys. 49, 972 (2019), arXiv:1901.01731 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  6. [6]

    An asymptotically safe guide to quantum gravity and matter

    A. Eichhorn, Front. Astron. Space Sci.5, 47 (2019), arXiv:1810.07615 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  7. [7]

    S. Sen, C. Wetterich, and M. Yamada, J. High Energy Phys. 03, 130 (2022), arXiv:2111.04696 [hep-th]

    work page arXiv 2022

  8. [8]

    Asymptotic safety of quantum gravity beyond Ricci scalars

    K. Falls, C. R. King, D. F. Litim, K. Nikolakopou- los, and C. Rahmede, Phys. Rev. D97, 086006 (2018), arXiv:1801.00162 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  9. [9]

    Rachwal, Universe8, 229 (2022), arXiv:2204.09858 [hep-th]

    L. Rachwal, Universe8, 229 (2022), arXiv:2204.09858 [hep-th]

    work page arXiv 2022

  10. [10]

    M. B. Green, J. H. Schwarz, and E. Witten,Superstring Theory Vol. 1: 25th Anniversary Edition(Cambridge University Press, 2012)

    work page 2012

  11. [11]

    M. B. Green, J. H. Schwarz, and E. Witten,Superstring Theory Vol. 2: 25th Anniversary Edition(Cambridge University Press, 2012)

    work page 2012

  12. [12]

    Polchinski, String Theory (Cambridge University Press, 1998)

    J. Polchinski, String Theory (Cambridge University Press, 1998)

    work page 1998

  13. [13]

    Ashtekar and E

    A. Ashtekar and E. Bianchi, Rep. Prog. Phys.84, 042001 (2021), arXiv:2104.04394 [gr-qc]

    work page arXiv 2021

  14. [14]

    Thiemann,Modern Canonical Quantum General Rel- ativity (Cambridge University Press, 2007)

    T. Thiemann,Modern Canonical Quantum General Rel- ativity (Cambridge University Press, 2007)

    work page 2007

  15. [15]

    Loll, Class

    R. Loll, Class. Quantum Grav. 37, 013002 (2020), arXiv:1905.08669 [hep-th]

    work page arXiv 2020

  16. [16]

    Ambjørn and R

    J. Ambjørn and R. Loll (2024) arXiv:2401.09399 [hep- th]

    work page arXiv 2024

  17. [17]

    Membranes at Quantum Criticality

    P. Horava, J. High Energy Phys. 03, 020 (2009), arXiv:0812.4287 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  18. [18]

    Quantum Gravity at a Lifshitz Point

    P. Horava, Phys. Rev. D 79, 084008 (2009), arXiv:0901.3775 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  19. [19]

    C. D. Hoyle, D. J. Kapner, B. R. Heckel, E. G. Adel- berger, J. H. Gundlach, U. Schmidt, and H. E. Swanson, Phys. Rev. D70, 042004 (2004), arXiv:hep-ph/0405262

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  20. [20]

    Touboulet al

    P. Touboulet al. (MICROSCOPE), Phys. Rev. Lett. 129, 121102 (2022), arXiv:2209.15487 [gr-qc]

    work page arXiv 2022

  21. [21]

    A. M. Sirunyanet al.(CMS), J. High Energy Phys.01, 163 (2021), arXiv:2007.05658 [hep-ex]

    work page arXiv 2021

  22. [22]

    Levi, Rep

    M. Levi, Rep. Prog. Phys. 83, 075901 (2020), arXiv:1807.01699 [hep-th]

    work page arXiv 2020

  23. [23]

    Chern-Simons Modified General Relativity

    S. Alexander and N. Yunes, Phys. Rep.480, 1 (2009), arXiv:0907.2562 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  24. [24]

    J. F. Donoghue, Phys. Rev. D50, 3874 (1994), arXiv:gr- qc/9405057

    work page arXiv 1994

  25. [25]

    J. F. Donoghue, AIP Conf. Proc. 1483, 73 (2012), arXiv:1209.3511 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  26. [26]

    J. F. Donoghue and B. R. Holstein, J. Phys. G42, 103102 (2015), arXiv:1506.00946 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  27. [27]

    J. F. Donoghue, in Handbook of Quantum Gravity (Springer, 2023) arXiv:2211.09902 [hep-th]

    work page arXiv 2023

  28. [28]

    Effective field theory from modified gravity with massive modes

    S. Capozziello, M. De Laurentis, M. Paolella, and G. Ric- ciardi, Int. J. Geom. Meth. Mod. Phys.12, 1550004 (2015), arXiv:1311.6319 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  29. [29]

    C. P. Burgess, Living Rev. Relativ.7, 5 (2004), arXiv:gr- qc/0311082

    work page arXiv 2004

  30. [30]

    Fundamental Theoretical Bias in Gravitational Wave Astrophysics and the Parameterized Post-Einsteinian Framework

    N. Yunes and F. Pretorius, Phys. Rev. D80, 122003 (2009), arXiv:0909.3328 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  31. [31]

    A Parametrized post-Einsteinian Framework for Gravitational Wave Bursts

    N. Loutrel, N. Yunes, and F. Pretorius, Phys. Rev. D 90, 104010 (2014), arXiv:1404.0092 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  32. [32]

    Loutrel, P

    N. Loutrel, P. Pani, and N. Yunes, Phys. Rev. D107, 044046 (2023), arXiv:2210.10571 [gr-qc]

    work page arXiv 2023

  33. [33]

    Tahura and K

    S. Tahura and K. Yagi, Phys. Rev. D 98, 084042 (2018), [Erratum: Phys.Rev.D 101, 109902 (2020)], arXiv:1809.00259 [gr-qc]

    work page arXiv 2018

  34. [34]

    C. M. Will, Living Rev. Relativ. 17, 4 (2014), arXiv:1403.7377 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  35. [35]

    Hohmann, in Modified Gravity and Cosmology (Springer, 2022)

    M. Hohmann, in Modified Gravity and Cosmology (Springer, 2022)

    work page 2022

  36. [36]

    Damour and N

    T. Damour and N. Deruelle, Annales de L’Institut Henri Poincare Section (A) Physique Theorique43, 107 (1985)

    work page 1985

  37. [37]

    Damour and N

    T. Damour and N. Deruelle, Annales de L’Institut Henri Poincare Section (A) Physique Theorique44, 263 (1986)

    work page 1986

  38. [38]

    Damour and J

    T. Damour and J. H. Taylor, Phys. Rev. D45, 1840 (1992)

    work page 1992

  39. [39]

    Theoretical Physics Implications of the Binary Black-Hole Mergers GW150914 and GW151226

    N. Yunes, K. Yagi, and F. Pretorius, Phys. Rev. D94, 084002 (2016), arXiv:1603.08955 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  40. [40]

    Carson and K

    Z. Carson and K. Yagi, inHandbook of Gravitational Wave Astronomy(Springer, 2022) arXiv:2011.02938 [gr- qc]

    work page arXiv 2022

  41. [41]

    Constraining Lorentz-violating, Modified Dispersion Relations with Gravitational Waves

    S. Mirshekari, N. Yunes, and C. M. Will, Phys. Rev. D 85, 024041 (2012), arXiv:1110.2720 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  42. [42]

    I. M. Romero-Shaw, P. D. Lasky, and E. Thrane, As- trophys. J. 940, 171 (2022), arXiv:2206.14695 [astro- ph.HE]

    work page arXiv 2022

  43. [43]

    Romero-Shaw, J

    I. Romero-Shaw, J. Stegmann, H. Tagawa, D. Gerosa, J. Samsing, N. Gupte, and S. R. Green, (2025), arXiv:2506.17105 [astro-ph.HE]

    work page arXiv 2025

  44. [44]

    Evidence for eccentricity in the population of binary black holes observed by LIGO-Virgo-KAGRA

    N. Gupteet al., (2024), arXiv:2404.14286 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  45. [45]

    Abbott et al

    R. Abbott et al. (LIGO Scientific, Virgo), Phys. Rev. Lett. 125, 101102 (2020), arXiv:2009.01075 [gr-qc]

    work page arXiv 2020

  46. [46]

    Gamba, M

    R. Gamba, M. Breschi, G. Carullo, S. Albanesi, P. Ret- tegno, S. Bernuzzi, and A. Nagar, Nat. Astron.7, 11 (2023), arXiv:2106.05575 [gr-qc]

    work page arXiv 2023

  47. [47]

    Ma and N

    S. Ma and N. Yunes, Phys. Rev. D100, 124032 (2019), arXiv:1908.07089 [gr-qc]

    work page arXiv 2019

  48. [48]

    Moore and N

    B. Moore and N. Yunes, Class. Quantum Grav.37, 165006 (2020), arXiv:2002.05775 [gr-qc]

    work page arXiv 2020

  49. [49]

    Guptaet al., SciPost Phys

    A. Guptaet al., SciPost Phys. Comm. Rep.5, (2024), arXiv:2405.02197 [gr-qc]

    work page arXiv 2024

  50. [50]

    Saini, M

    P. Saini, M. Favata, and K. G. Arun, Phys. Rev. D106, 084031 (2022), arXiv:2203.04634 [gr-qc]

    work page arXiv 2022

  51. [51]

    S. A. Bhat, P. Saini, M. Favata, and K. G. Arun, Phys. Rev. D107, 024009 (2023), arXiv:2207.13761 [gr-qc]

    work page arXiv 2023

  52. [52]

    Narayan, N

    P. Narayan, N. K. Johnson-McDaniel, and A. Gupta, Phys. Rev. D108, 064003 (2023), arXiv:2306.04068 [gr- qc]

    work page arXiv 2023

  53. [53]

    Saini, S

    P. Saini, S. A. Bhat, M. Favata, and K. G. Arun, Phys. Rev. D109, 084056 (2024), arXiv:2311.08033 [gr-qc]

    work page arXiv 2024

  54. [54]

    Wen, Astrophys

    L. Wen, Astrophys. J. 598, 419 (2003), arXiv:astro- ph/0211492

    work page arXiv 2003

  55. [55]

    Loutrel, Class

    N. Loutrel, Class. Quantum Grav.37, 075008 (2020), arXiv:1909.02143 [gr-qc]

    work page arXiv 2020

  56. [56]

    Loutrel, Class

    N. Loutrel, Class. Quantum Grav.38, 015005 (2021), arXiv:2003.13673 [gr-qc]

    work page arXiv 2021

  57. [57]

    L. S. Finn, Phys. Rev. D46, 5236 (1992), arXiv:gr- qc/9209010

    work page arXiv 1992

  58. [58]

    Gravitational Waves from Mergin Compact Binaries: How Accurately Can One Extract the Binary's Parameters from the Inspiral Waveform?

    C. Cutler and E. E. Flanagan, Phys. Rev. D49, 2658 (1994), arXiv:gr-qc/9402014

    work page internal anchor Pith review Pith/arXiv arXiv 1994

  59. [59]

    C. M. Will, Phys. Rev. D57, 2061 (1998), arXiv:gr- qc/9709011. 18

    work page arXiv 2061

  60. [60]

    V. A. Rubakov and P. G. Tinyakov, Phys. Usp.51, 759 (2008), arXiv:0802.4379 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  61. [61]

    Theoretical Aspects of Massive Gravity

    K. Hinterbichler, Rev. Mod. Phys. 84, 671 (2012), arXiv:1105.3735 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  62. [62]

    Massive Gravity

    C. de Rham, Living Rev. Relativ. 17, 7 (2014), arXiv:1401.4173 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  63. [63]

    A. S. Sefiedgar, K. Nozari, and H. R. Sepangi, Phys. Lett. B696, 119 (2011), arXiv:1012.1406 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  64. [64]

    Testable scenario for Relativity with minimum-length

    G. Amelino-Camelia, Phys. Lett. B510, 255 (2001), arXiv:hep-th/0012238

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  65. [65]

    Lorentz invariance with an invariant energy scale

    J. Magueijo and L. Smolin, Phys. Rev. Lett.88, 190403 (2002), arXiv:hep-th/0112090

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  66. [66]

    Amelino-Camelia, Nature418, 34 (2002), arXiv:gr- qc/0207049

    G. Amelino-Camelia, Nature418, 34 (2002), arXiv:gr- qc/0207049

    work page arXiv 2002

  67. [67]

    S. I. Vacaru, Gen. Relat. Gravit. 44, 1015 (2012), arXiv:1010.5457 [math-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  68. [68]

    Gravitational Radiation in Horava Gravity

    D. Blas and H. Sanctuary, Phys. Rev. D84, 064004 (2011), arXiv:1105.5149 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  69. [69]

    Fractal universe and quantum gravity

    G. Calcagni, Phys. Rev. Lett. 104, 251301 (2010), arXiv:0912.3142 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  70. [70]

    Geometry of fractional spaces

    G. Calcagni, Adv. Theor. Math. Phys.16, 549 (2012), arXiv:1106.5787 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  71. [71]

    Geometry and field theory in multi-fractional spacetime

    G. Calcagni, J. High Energy Phys. 01, 065 (2012), arXiv:1107.5041 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  72. [72]

    Lorentz violations in multifractal spacetimes

    G. Calcagni, Eur. Phys. J. C 77, 291 (2017), arXiv:1603.03046 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  73. [73]

    V. A. Kostelecký and M. Mewes, Phys. Lett. B757, 510 (2016), arXiv:1602.04782 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  74. [74]

    Wahlquist, Gen

    H. Wahlquist, Gen. Relat. Gravit.19, 1101 (1987)

    work page 1987

  75. [75]

    Gravitational waves from eccentric compact binaries: Reduction in signal-to-noise ratio due to nonoptimal signal processing

    K. Martel and E. Poisson, Phys. Rev. D60, 124008 (1999), arXiv:gr-qc/9907006

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  76. [76]

    Moreno-Garrido, E

    C. Moreno-Garrido, E. Mediavilla, and J. Buitrago, Mon. Not. R. Astron. Soc.274, 115 (1995)

    work page 1995

  77. [77]

    A Fourier Domain Waveform for Non-Spinning Binaries with Arbitrary Eccentricity

    B. Moore, T. Robson, N. Loutrel, and N. Yunes, Class. Quantum Grav.35, 235006 (2018), arXiv:1807.07163 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  78. [78]

    Turner, Astrophys

    M. Turner, Astrophys. J.216, 610 (1977)

    work page 1977

  79. [79]

    Spin-Precessing Black Hole Binaries in Dynamical Chern-Simons Gravity

    N. Loutrel, T. Tanaka, and N. Yunes, Phys. Rev. D98, 064020 (2018), arXiv:1806.07431 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  80. [80]

    Abramowitz and I

    M. Abramowitz and I. A. Stegun,Handbook of mathemat- ical functions with formulas, graphs, and mathematical tables (Dover Publications, 1965)

    work page 1965

Showing first 80 references.