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arxiv: 2605.30369 · v1 · pith:5PGJ3RDHnew · submitted 2026-05-18 · 🌌 astro-ph.HE · astro-ph.IM· gr-qc

Reconciling GW170817 and GW190814 with a Nonmonotonic Sound-Speed Equation of State

Marlon M. S. Mendes , Odilon Louren\c{c}o da Silva Filho , C\'esar H. Lenzi This is my paper

Pith reviewed 2026-06-30 18:15 UTC · model grok-4.3

classification 🌌 astro-ph.HE astro-ph.IMgr-qc
keywords neutron starsgravitational wavesequation of statesound speedGW170817GW190814general relativity
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0 comments X

The pith

Double-peaked sound speeds reconcile GW170817 and GW190814 within general relativity.

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

The paper shows that the apparent conflict between the two gravitational-wave events can be resolved inside standard general relativity by allowing the equation of state of dense matter to have a non-monotonic sound-speed profile. A search algorithm called the Constrained Evolutionary TOV Discovery pipeline locates a large family of causal equations of state that simultaneously satisfy the mass, radius, and tidal-deformability bounds reported for both mergers. The resulting basin contains roughly fourteen thousand distinct equations of state whose sound speeds rise to two distinct peaks, each reaching 0.86–0.99 times the square of the speed of light.

Core claim

The GW170817-GW190814 tension can be reconciled within General Relativity by a structured causal EoS basin found with a Constrained Evolutionary TOV Discovery pipeline (CETD). The basin contains ~1.4x10^4 unique EoS with M_max = 2.3-2.8 M_sun, R_1.4 = 11.97-12.29 km, Lambda_1.4 <= 580, and double-peaked sound speeds reaching c_s^2/c^2 = 0.86-0.99.

What carries the argument

The Constrained Evolutionary TOV Discovery (CETD) pipeline, which systematically generates and filters causal equations of state against gravitational-wave constraints to locate a connected basin of viable solutions.

If this is right

  • Roughly 14,000 distinct causal equations of state satisfy the joint constraints from both events.
  • Maximum neutron-star masses lie between 2.3 and 2.8 solar masses.
  • Radii of 1.4-solar-mass stars are confined to 11.97–12.29 km.
  • Tidal deformabilities of 1.4-solar-mass stars do not exceed 580.
  • Sound-speed profiles must exhibit two distinct peaks reaching 0.86–0.99 c².

Where Pith is reading between the lines

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

  • Future radius or tidal measurements could further restrict the allowed locations and heights of the sound-speed peaks.
  • The same search strategy could be applied to other pairs of apparently conflicting compact-object observations.
  • Double-peaked sound speeds may correspond to one or more phase transitions inside neutron-star cores.
  • If the basin survives additional data, it would indicate that general relativity alone is sufficient to describe both events without modified-gravity extensions.

Load-bearing premise

The Constrained Evolutionary TOV Discovery pipeline correctly and exhaustively samples the space of causal equations of state without introducing selection bias or missing observationally allowed solutions.

What would settle it

Detection of a neutron star with mass above 2.8 solar masses, or a 1.4-solar-mass star whose radius lies outside the 11.97–12.29 km window, would falsify the existence of the reported EoS basin.

Figures

Figures reproduced from arXiv: 2605.30369 by C\'esar H. Lenzi, Marlon M. S. Mendes, Odilon Louren\c{c}o da Silva Filho.

Figure 1
Figure 1. Figure 1: FIG. 1. Stage 2 mass amplification. (a) Generational screening of the candidate pool through TOV, causal, astrophysical, [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Causal equation-of-state solutions grouped by maximum-mass bin. Panel (a) shows the corresponding mass–radius [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
read the original abstract

We show that the GW170817-GW190814 tension can be reconciled within General Relativity by a structured causal EoS basin found with a Constrained Evolutionary TOV Discovery pipeline (CETD). The basin contains ~1.4x10^4 unique EoS with M_max = 2.3-2.8 M_sun, R_1.4 = 11.97-12.29 km, Lambda_1.4 <= 580, and double-peaked sound speeds reaching c_s^2/c^2 = 0.86-0.99.

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 manuscript claims that the tension between GW170817 and GW190814 can be reconciled within General Relativity by a structured causal EoS basin containing ~1.4×10^4 unique equations of state, discovered via a Constrained Evolutionary TOV Discovery (CETD) pipeline. These EoS satisfy M_max = 2.3-2.8 M_⊙, R_1.4 = 11.97-12.29 km, Λ_1.4 ≤ 580, and exhibit double-peaked sound speeds with c_s²/c² reaching 0.86-0.99 while remaining causal.

Significance. If the CETD pipeline is shown to exhaustively sample the space of causal EoS without selection bias or artificial clustering, the result would be significant: it would demonstrate that non-monotonic sound-speed profiles can simultaneously accommodate the relatively compact radius and low tidal deformability from GW170817 with the high maximum mass from GW190814, supplying a large, observationally viable sample for neutron-star modeling.

major comments (1)
  1. [Abstract] Abstract: the central claim that the CETD pipeline discovers a genuine basin of ~1.4×10^4 EoS satisfying both GW events rests on the unverified assumptions that the evolutionary algorithm (1) enforces the TOV equations and causality at every generation, (2) samples the full space of causal EoS without convergence bias, and (3) does not miss viable solutions outside the reported basin. No cross-check against standard parametrizations (piecewise polytropes or spectral representations) is described, rendering the reconciliation claim unverifiable from the supplied text.

Simulated Author's Rebuttal

1 responses · 1 unresolved

We thank the referee for their thoughtful review and the opportunity to address the concerns regarding verification of the CETD pipeline. We respond point by point below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that the CETD pipeline discovers a genuine basin of ~1.4×10^4 EoS satisfying both GW events rests on the unverified assumptions that the evolutionary algorithm (1) enforces the TOV equations and causality at every generation, (2) samples the full space of causal EoS without convergence bias, and (3) does not miss viable solutions outside the reported basin. No cross-check against standard parametrizations (piecewise polytropes or spectral representations) is described, rendering the reconciliation claim unverifiable from the supplied text.

    Authors: We thank the referee for highlighting these points. Section 2 details that the CETD algorithm parametrizes the squared sound speed directly with an explicit upper bound of 1 to enforce causality at every generation; candidate profiles are then integrated via the TOV equations and discarded if they fail to yield stable configurations. Population diversity is maintained through explicit mutation and crossover operators, with convergence monitored via the standard deviation of the two sound-speed peak locations across generations (Figure 4). We agree that exhaustive coverage of the full causal EoS space cannot be rigorously proven for any finite sampling method. A direct comparison to piecewise-polytropic or spectral representations is not included in the current text; we will add a concise consistency check in the revised manuscript. revision: partial

standing simulated objections not resolved
  • Demonstrating that the evolutionary algorithm samples the entire space of causal EoS without convergence bias or missing viable solutions outside the reported basin.

Circularity Check

0 steps flagged

No circularity: numerical search result, not derivation by construction

full rationale

The paper reports a numerical discovery via the CETD evolutionary pipeline of a large set of causal EoS satisfying the stated GW170817 and GW190814 constraints plus causality. This is a search outcome in parameter space rather than a claimed first-principles derivation or prediction that reduces to its inputs by definition. No equations, self-citations, or load-bearing steps are exhibited in the supplied text that would trigger any of the enumerated circularity patterns. The result that such a non-monotonic basin exists is independent of the search method itself provided the pipeline enforces TOV, causality, and the observational bounds without embedding the target conclusion.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only; the only explicit constraint mentioned is causality of the EoS. No free parameters, additional axioms, or invented entities are described.

axioms (1)
  • domain assumption Sound speed must satisfy c_s <= c everywhere (causality)
    Stated requirement for the EoS basin in the abstract.

pith-pipeline@v0.9.1-grok · 5649 in / 1146 out tokens · 31246 ms · 2026-06-30T18:15:53.061849+00:00 · methodology

discussion (0)

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Works this paper leans on

56 extracted references · 29 canonical work pages · 13 internal anchors

  1. [1]

    B. P. Abbottet al., GW170817: Observation of gravita- tional waves from a binary neutron star inspiral, Physical Review Letters119, 161101 (2017)

    2017

  2. [2]

    B. P. Abbottet al., GW170817: Measurements of neu- tron star radii and equation of state, Physical Review Letters121, 161101 (2018)

    2018

  3. [3]

    C. D. Capano, I. Tews, S. M. Brown, B. Margalit, S. De, S. Kumar, D. A. Brown, B. Krishnan, and S. Reddy, Stringent constraints on neutron-star radii from multi- messenger observations and nuclear theory, Nature As- tronomy4, 625 (2020)

    2020

  4. [4]

    Abbottet al., GW190814: Gravitational waves from the coalescence of a 23m ⊙ black hole with a 2.6m ⊙ compact object, The Astrophysical Journal Letters896, L44 (2020)

    R. Abbottet al., GW190814: Gravitational waves from the coalescence of a 23m ⊙ black hole with a 2.6m ⊙ compact object, The Astrophysical Journal Letters896, L44 (2020)

    2020

  5. [5]

    A. G. Abacet al.(LIGO Scientific Collaboration and Virgo Collaboration and KAGRA Collaboration), Ob- servation of gravitational waves from the coalescence of a 2.5–4.5M⊙ compact object and a neutron star, The Astrophysical Journal Letters970, L34 (2024)

    2024

  6. [6]

    H. Tan, J. Noronha-Hostler, and N. Yunes, Neutron star equation of state in light of GW190814, Physical Review Letters125, 261104 (2020)

    2020

  7. [7]

    F. J. Fattoyev, C. J. Horowitz, J. Piekarewicz, and B. Reed, GW190814: Impact of a 2.6 solar mass neu- tron star on the nucleonic equations of state, Physical Review C102, 065805 (2020)

    2020

  8. [8]

    Nathanail, E

    A. Nathanail, E. R. Most, and L. Rezzolla, GW170817 and GW190814: Tension on the maximum mass, The Astrophysical Journal Letters908, L28 (2021)

    2021

  9. [9]

    Annala, T

    E. Annala, T. Gorda, A. Kurkela, J. Nättilä, and A. Vuorinen, Evidence for quark-matter cores in massive neutron stars, Nature Physics16, 907 (2020)

    2020

  10. [10]

    Kojo, Qcd equations of state and speed of sound in neutron stars, AAPPS Bulletin31, 11 (2021)

    T. Kojo, Qcd equations of state and speed of sound in neutron stars, AAPPS Bulletin31, 11 (2021)

    2021

  11. [11]

    N. Yao, A. Sorensen, V. Dexheimer, and J. Noronha- Hostler, Structure in the speed of sound: From neutron stars to heavy-ion collisions, Physical Review C109, 065803 (2024), arXiv:2311.18819

    work page arXiv 2024

  12. [12]

    K. C. Gendreau, Z. Arzoumanian, P. W. Adkins, et al., The Neutron star Interior Composition Explorer (NICER): Design and development, inSpace Telescopes and Instrumentation 2016: Ultraviolet to Gamma Ray, Proc. SPIE, Vol. 9905, edited by J.-W. A. den Herder, T. Takahashi, and M. Bautz (2016) p. 99051H

    2016

  13. [13]

    M. C. Miller, F. K. Lamb, A. J. Dittmann,et al., The ra- diusofPSRJ0740+6620fromNICERandXMM-Newton data, The Astrophysical Journal Letters918, L28 (2021)

    2021

  14. [14]

    T. E. Riley, A. L. Watts, P. S. Ray,et al., A NICER view of the massive pulsar PSR J0740+6620 informed by radio timing and XMM-Newton spectroscopy, The Astrophys- ical Journal Letters918, L27 (2021)

    2021

  15. [15]

    B. T. Reed, F. J. Fattoyev, C. J. Horowitz, and J. Piekarewicz, Implications of PREX-2 on the equation of state of neutron-rich matter, Physical Review Letters 126, 172503 (2021)

    2021

  16. [16]

    F. J. Fattoyev, J. Piekarewicz, and C. J. Horowitz, Neu- tron skins and neutron stars in the multimessenger era, Physical Review Letters120, 172702 (2018)

    2018

  17. [17]

    Zhou, Bayesian evidence for two peaks in the sound speed in cold dense QCD (2024), arXiv:2412.08760 [nucl- th]

    D. Zhou, Bayesian evidence for two peaks in the sound speed in cold dense QCD (2024), arXiv:2412.08760 [nucl- th]

    work page arXiv 2024

  18. [18]

    Cai and B.-A

    B.-J. Cai and B.-A. Li, Strong gravity extruding peaks in speed of sound profiles of massive neutron stars, Physical Review D109, 083015 (2024), arXiv:2311.13037

    work page arXiv 2024

  19. [19]

    Mroczek, M

    D. Mroczek, M. C. Miller, J. Noronha-Hostler, and N. Yunes, Nontrivial features in the speed of sound inside neutron stars, Physical Review D110, 123009 (2024), arXiv:2309.02345 [astro-ph.HE]

    work page arXiv 2024

  20. [20]

    Ecker and L

    C. Ecker and L. Rezzolla, A general, scale-independent description of the sound speed in neutron stars, The Astrophysical Journal Letters939, L35 (2022), arXiv:2207.04417 [astro-ph.HE]

    work page arXiv 2022

  21. [21]

    J. S. Read, B. D. Lackey, B. J. Owen, and J. L. Fried- man,Constraintsonaphenomenologicallyparameterized neutron-star equation of state, Physical Review D79, 124032 (2009), arXiv:0812.2163 [astro-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  22. [22]

    R.C.Tolman,Staticsolutionsofeinstein’sfieldequations for spheres of fluid, Physical Review55, 364 (1939)

    1939

  23. [23]

    J. R. Oppenheimer and G. M. Volkoff, On massive neu- tron cores, Physical Review55, 374 (1939)

    1939

  24. [24]

    B. P. Abbottet al.(LIGO Scientific Collaboration and Virgo Collaboration), Properties of the binary neutron star merger GW170817, Physical Review X9, 011001 (2019), arXiv:1805.11579 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  25. [25]

    M. C. Miller, F. K. Lamb, A. J. Dittmann,et al., PSR J0030+0451 mass and radius from NICER data and implications for the properties of neutron star mat- ter, The Astrophysical Journal Letters887, L24 (2019), arXiv:1912.05705 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  26. [26]

    T. E. Riley, A. L. Watts, S. Bogdanov,et al., A NICER view of PSR J0030+0451: Millisecond pulsar parameter estimation, The Astrophysical Journal Letters887, L21 (2019), arXiv:1912.05702 [astro-ph.HE]

    work page arXiv 2019

  27. [27]

    P. B. Demorest, T. Pennucci, S. M. Ransom, M. S. E. Roberts, and J. W. T. Hessels, A two-solar-mass neu- tron star measured using shapiro delay, Nature467, 1081 (2010)

    2010

  28. [28]

    A Massive Pulsar in a Compact Relativistic Binary

    J. Antoniadis, P. C. C. Freire, N. Wex,et al., A mas- sive pulsar in a compact relativistic binary, Science340, 1233232 (2013), arXiv:1304.6875 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  29. [29]

    H. T. Cromartie, E. Fonseca, S. M. Ransom,et al., Rela- tivistic shapiro delay measurements of an extremely mas- sive millisecond pulsar, Nature Astronomy4, 72 (2020), arXiv:1904.06759 [astro-ph.HE]

    work page arXiv 2020

  30. [30]

    Fonseca, H

    E. Fonseca, H. T. Cromartie, T. T. Pennucci,et al., Refined mass and geometric measurements of the high- mass PSR J0740+6620, The Astrophysical Journal Let- ters915, L12 (2021), arXiv:2104.00880 [astro-ph.HE]

    work page arXiv 2021

  31. [31]

    Efron, Bootstrap methods: Another look at the jack- knife, The Annals of Statistics7, 1 (1979)

    B. Efron, Bootstrap methods: Another look at the jack- knife, The Annals of Statistics7, 1 (1979)

    1979

  32. [32]

    Efron and R

    B. Efron and R. J. Tibshirani,An Introduction to the Bootstrap(Chapman and Hall, New York, 1993)

    1993

  33. [33]

    Tidal Love numbers of neutron stars

    T. Hinderer, Tidal love numbers of neutron stars, The Astrophysical Journal677, 1216 (2008), arXiv:0711.2420 [astro-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  34. [34]

    I-Love-Q

    K. Yagi and N. Yunes, I-Love-Q: Unexpected universal relations for neutron stars and quark stars, Science341, 365 (2013), arXiv:1302.4499 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  35. [35]

    I-Love-Q Relations in Neutron Stars and their Applications to Astrophysics, Gravitational Waves and Fundamental Physics

    K. Yagi and N. Yunes, I-Love-Q relations in neutron stars and their applications to astrophysics, gravitational waves, and fundamental physics, Physical Review D88, 6 023009 (2013), arXiv:1303.1528 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  36. [36]

    Komoltsev and A

    O. Komoltsev and A. Kurkela, How perturbative QCD constrains the equation of state at neutron-star den- sities, Physical Review Letters128, 202701 (2022), arXiv:2111.05350 [nucl-th]

    work page arXiv 2022

  37. [37]

    Bedaque and A

    P. Bedaque and A. W. Steiner, Sound velocity bound and neutron stars, Physical Review Letters114, 031103 (2015)

    2015

  38. [38]

    S. Huth, P. T. H. Pang, I. Tews, T. Dietrich, A. Le Fèvre, A. Schwenk, W. Trautmann, K. Agarwal, M. Bulla, M. W. Coughlin, and C. Van Den Broeck, Constraining neutron-star matter with microscopic and macroscopic collisions, Nature606, 276 (2022)

    2022

  39. [39]

    P.T.H.Pang, T.Dietrich, M.W.Coughlin,et al.,Anup- dated nuclear-physics and multi-messenger astrophysics framework for binary neutron star mergers, Nature Com- munications14, 8352 (2023)

    2023

  40. [40]

    R. D. Sorkin, A criterion for the onset of instability at a turning point, The Astrophysical Journal249, 254 (1981)

    1981

  41. [41]

    J. L. Friedman, J. R. Ipser, and R. D. Sorkin, Turning- point method for axisymmetric stability of rotating rela- tivistic stars, The Astrophysical Journal325, 722 (1988)

    1988

  42. [42]

    Chandrasekhar, Dynamical instability of gaseous massesapproachingtheschwarzschildlimitingeneralrel- ativity, The Astrophysical Journal140, 417 (1964)

    S. Chandrasekhar, Dynamical instability of gaseous massesapproachingtheschwarzschildlimitingeneralrel- ativity, The Astrophysical Journal140, 417 (1964)

    1964

  43. [43]

    J. M. Bardeen, K. S. Thorne, and D. W. Meltzer, A cat- alogue of methods for studying the normal modes of ra- dial pulsation of general-relativistic stellar models, The Astrophysical Journal145, 505 (1966)

    1966

  44. [44]

    K. D. Kokkotas and J. Ruoff, Radial oscillations of rela- tivisticstars,Astronomy&Astrophysics366,565(2001), arXiv:gr-qc/0011093

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  45. [45]

    A unified equation of state of dense matter and neutron star structure

    F. Douchin and P. Haensel, A unified equation of state of dense matter and neutron star structure, Astronomy & Astrophysics380, 151 (2001), arXiv:astro-ph/0111092

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  46. [46]

    CompOSE - CompStar Online Supernovae Equations of State

    S. Typel, M. Oertel, and T. Klähn, Compose compstar online supernova equations of state harmonising the con- cert of nuclear physics and astrophysics, Physics of Par- ticles and Nuclei46, 633 (2015), arXiv:1307.5715 [astro- ph.SR]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  47. [47]

    J. W. Moffat, Modified gravity (MOG) and heavy neu- tron star in mass gap (2020), arXiv:2008.04404 [gr-qc]

    work page arXiv 2020

  48. [48]

    A. V. Astashenok, S. Capozziello, S. D. Odintsov, and V. K. Oikonomou, Extended gravity description for the GW190814 supermassive neutron star, Physics Letters B 811, 135910 (2020), arXiv:2008.10884 [gr-qc]

    work page arXiv 2020

  49. [49]

    R. C. Nunes, J. G. Coelho, and J. C. N. de Araujo, Weighing massive neutron star with screening gravity: a lookonPSRJ0740+6620andGW190814secondarycom- ponent, European Physical Journal C80, 1115 (2020), arXiv:2008.10395 [astro-ph.HE]

    work page arXiv 2020

  50. [50]

    Lin, X.-N

    R.-H. Lin, X.-N. Chen, and X.-H. Zhai, Realistic neutron star models inf(T)gravity, European Physical Journal C82, 308 (2022), arXiv:2109.00191 [gr-qc]

    work page arXiv 2022

  51. [51]

    Charmousis, A

    C. Charmousis, A. Lehébel, E. Smyrniotis, and N. Ster- gioulas, Astrophysical constraints on compact objects in 4D Einstein–Gauss–Bonnet gravity, Journal of Cos- mology and Astroparticle Physics2022(02), 033, arXiv:2109.01149 [gr-qc]

    work page arXiv

  52. [52]

    Reyes and J

    C. Reyes and J. Sakstein, Parameterized post-Tolman– Oppenheimer–Volkoff framework for screened modified gravity with an application to the secondary component of GW190814, Physical Review D109, 084080 (2024), arXiv:2403.03399 [gr-qc]

    work page arXiv 2024

  53. [53]

    Science Case for the Einstein Telescope

    M. Maggioreet al., Science case for the Einstein Tele- scope, Journal of Cosmology and Astroparticle Physics 2020(03), 050, arXiv:1912.02622 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2020

  54. [54]

    Cosmic Explorer: The U.S. Contribution to Gravitational-Wave Astronomy beyond LIGO

    D. Reitzeet al., Cosmic Explorer: The U.S. contribution to gravitational-wave astronomy beyond LIGO, Bulletin of the American Astronomical Society51, 035 (2019), arXiv:1907.04833 [astro-ph.IM]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  55. [55]

    Identifying a first-order phase transition in neutron star mergers through gravitational waves

    A. Bauswein, N.-U. F. Bastian, D. B. Blaschke, K. Chatziioannou, J. A. Clark, T. Fischer, and M. Oertel, Identifying a first-order phase transition in neutron-star mergers through gravitational waves, Physical Review Letters122, 061102 (2019), arXiv:1809.01116 [astro- ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  56. [56]

    Bernuzzi, Neutron star merger remnants, General Rel- ativity and Gravitation52, 108 (2020), arXiv:2004.06419 [astro-ph.HE]

    S. Bernuzzi, Neutron star merger remnants, General Rel- ativity and Gravitation52, 108 (2020), arXiv:2004.06419 [astro-ph.HE]

    work page arXiv 2020