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Radial Oscillations of Viscous Stars

T0 review · 2 major / 5 minor · reviewed 2026-07-13 · grok-4.5

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Pith's one-line read Viscosity damps neutron-star radial modes in milliseconds and can erase their oscillation frequency at high bulk viscosity, but does not stop gravitational collapse.

desk verdict Solid linear numerics on viscous radial modes with public code; the percent-level shifts and overdamping are robust, while the BDNK threshold claim is thinner than the rest. read the letter →

arxiv 2603.23622 v2 pith:AGICBWK7 submitted 2026-03-24 gr-qc astro-ph.HE

Lennox S. Keeble , Jaime Redondo-Yuste This is my paper · ORCID
classification gr-qcastro-ph.HE
keywords neutronstarsradialoscillationsbulkviscosityEckarthydrodynamicsBDNKgravitationalcollapseasteroseismologypolytropic
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Neutron-star oscillation modes are a prime target for future gravitational-wave detectors because they carry information about the dense nuclear matter inside the star. This paper asks what bulk viscosity does to the purely radial modes of cold, polytropic stars. Working to linear order in two first-order relativistic hydrodynamics theories—one acausal (Eckart) and one causal (BDNK)—the authors show that viscosity damps the modes on millisecond timescales and shifts their frequencies by up to the percent level at bulk viscosities of order 10^30 g/cm/s. At still higher viscosity the fundamental frequency falls to zero and the mode becomes overdamped. Viscosity cannot stabilize a star that is already unstable to collapse, though it can slow the collapse rate dramatically and, in the causal theory, slightly moves the critical density. The results supply concrete numbers for viscous asteroseismology with next-generation detectors.

What carries the argument

Linearized radial master equations (or constrained wave-plus-constraint systems) for the Eckart and BDNK stress-energy tensors, solved both as frequency-domain eigenvalue problems and as time-domain evolutions of single-mode and Gaussian initial data on polytropic TOV backgrounds.

What would settle it

A full frequency-domain eigenvalue scan of BDNK stars across a dense grid of central densities and viscosities, or a nonlinear radial simulation that shows whether an inviscid-unstable configuration remains unstable once finite-amplitude and finite-temperature effects are restored.

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Extended reading notes

Core claim

Viscosity damps radial modes of cold polytropic neutron stars on millisecond timescales and produces fractional frequency shifts that grow with both compactness and viscosity, reaching the percent level for the fundamental mode near ζ ∼ 10^30 g/cm/s; for ζ ≳ 10^31 g/cm/s the frequency vanishes (overdamped). Viscosity in Eckart theory leaves the linear collapse threshold unchanged; numerical evidence indicates BDNK viscosity is likewise unable to prevent collapse while only slightly shifting the threshold.

Load-bearing premise

The stars are treated as cold barotropic polytropes with fixed shear-to-bulk ratio and zero heat conductivity, and all statements about stability are made only at linear order in spherical symmetry.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. The paper studies linear radial oscillations of cold, polytropic, spherically symmetric neutron stars in two first-order viscous hydrodynamics frameworks: Eckart and BDNK. Using both frequency-domain eigenvalue methods (Eckart) and time-domain evolutions (Eckart and BDNK), it reports that bulk viscosity damps radial modes on millisecond timescales and produces fractional frequency shifts that grow with compactness and viscosity, reaching the percent level for the fundamental mode near ζ ∼ 10^30 g cm^{-1} s^{-1}. For ζ ≳ 10^31 g cm^{-1} s^{-1} the fundamental frequency vanishes (overdamped). Viscosity in Eckart theory leaves the linear collapse threshold unchanged (consistent with prior analytic work) while slowing the instability rate; numerical evidence is offered that BDNK viscosity likewise cannot stabilize an unstable inviscid star but slightly shifts the threshold. Public code and extensive cross-checks (perfect-fluid recovery of Kokkotas & Ruoff, frame robustness, independent residuals) are provided.

Significance. If the results hold, the work supplies concrete, quantitative targets for viscous asteroseismology with third-generation detectors: percent-level frequency shifts and millisecond damping at post-merger viscosities, plus the existence of arbitrarily low-frequency overdamped radial modes. The public NeutronStarOscillations.jl package, the Eckart frequency-domain formulation, and the demonstrated agreement between Eckart and BDNK at moderate viscosity are reusable assets. The collapse analysis extends recent analytic stability criteria into the large-viscosity regime and supplies the first numerical indication of a BDNK threshold shift, even if that indication remains provisional.

major comments (2)
  1. [Sec. V.C, Fig. 7] Sec. V.C and Fig. 7: the claim that BDNK viscosity “slightly modifies the threshold of collapse” rests on three time-domain runs of Eckart-eigenvector initial data at ζ̂ = 10^{-3} near ε_c^* ≈ 5.663 × 10^{15} g cm^{-3}. No BDNK frequency-domain eigenvalue problem is solved; the constrained system (App. C) employs KO dissipation (coeff. 0.2) and already shows a numerical-viscosity plateau for ζ̂ ≲ 10^{-3} (Fig. 3). A 0.001 shift in critical density is comparable to the TOV termination tolerance (p = p_c imes 10^{-6}) and residual numerical dissipation. Either a systematic BDNK eigenvalue scan (or a carefully controlled resolution study that isolates the threshold) is needed, or the claim should be rephrased as a tentative indication pending further work.
  2. [Secs. II–III, Eq. (23)] Secs. II–III, Eq. (23): all quantitative results (percent-level shifts, overdamping at ζ ∼ 5 imes 10^{31}, collapse timescales) are obtained for two fixed cold polytropes with η = ζ/10 and zero heat conductivity. While the authors note this limitation, the abstract and conclusions present the numbers as generic for neutron-star viscosities. A short discussion of how the quoted thresholds and fractional shifts are expected to change under finite-temperature or tabulated EOS would strengthen the central claim.
minor comments (5)
  1. [Fig. 3] Fig. 3 caption and surrounding text: the faint plateau of the BDNK curves as ζ̂ o 0 is correctly attributed to numerical viscosity, but the figure itself would benefit from an explicit annotation or a higher-resolution inset so that readers do not misread the plateau as a physical effect.
  2. [Appendix B] Appendix B, Tables II–III: the perfect-fluid frequencies are stated to agree with Kokkotas & Ruoff (2001) to ≲ 1 %. Quoting the absolute differences (or a short comparison column) would make the validation more transparent.
  3. [Eq. (9)] Eq. (9) and the definition of L: the length scale that converts dimensionless transport coefficients into dimensionful viscosities is never given a concrete numerical value. Stating the choice used for the reported ζ_c values would aid reproducibility.
  4. [Sec. IV.B.2] Sec. IV.B.2: the Crank–Nicholson scheme and KO coefficient 0.2 are mentioned, but the precise form of the KO operator (and whether it is applied to all variables) is left implicit. A one-sentence clarification would help readers re-implement the code.
  5. [Sec. II] Typographical: “Einstein-NA VIER-STOKES” (Sec. II heading) and occasional missing spaces around “ζ∼” should be cleaned.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: eigenvalues and thresholds are obtained by direct numerical solution of the linearized Einstein–hydro equations, not by construction from fitted inputs or load-bearing self-citations.

full rationale

The paper derives the radial master equation (Eckart, Eqs. 15–18) and the constrained BDNK system (Sec. III.B.2 and App. C) from the Einstein equations plus the first-order stress-energy tensors, then extracts complex frequencies by frequency-domain matrix/shooting methods and by time-domain evolution of Gaussian or eigenvector initial data. The reported percent-level shifts, millisecond damping times, overdamping transition at ζ ≳ 10^31 g cm^{-3}, and the Eckart stability threshold are therefore outputs of those solves, cross-checked between domains and against the known inviscid spectrum of Kokkotas & Ruoff. The three BDNK frames and the two polytropes are free parameters whose variation is used only to demonstrate robustness; they are not tuned to force the claimed shifts. Citations to the authors’ earlier non-radial papers supply background on causality and non-radial modes but are not invoked as uniqueness theorems or as the sole justification for any central numerical result. The analytic consistency statement with Caballero & Yunes (external) is confirmatory, not definitional. Consequently the derivation chain is self-contained and non-circular.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The calculation rests on standard GR hydrodynamics plus two first-order viscous frames, cold polytropic EOS, linear spherical symmetry, and a handful of free transport parameters. No new particles or forces are introduced; the free parameters are conventional choices of EOS and frame that control the physical viscosity and causality regulators.

free parameters (4)
  • polytropic index n and constant κ = n=1,κ=100; n=0.8,κ=700
    Two fixed pairs (n=1, κ=100 km²) and (n=0.8, κ=700 km^{2.5}) define the entire family of background stars; results are reported only for these two EOS.
  • dimensionless bulk viscosity ˆζ (and η=ζ/10) = η=ζ/10; ˆζ scanned
    Controls the physical strength of dissipation; scanned over many orders of magnitude but fixed ratio η/ζ chosen by hand.
  • BDNK relaxation times ˆτ_ε, ˆτ_π, ˆτ_Q (frames A/B/C) = A:(1.5,15,20); B:(2,20,20); C:(3,25,25)
    Three discrete causal frames are chosen to satisfy the causality inequalities; results are shown to be robust but the specific numbers are free.
  • length scale L appearing in transport coefficients
    Sets the overall dimensionful scale of viscosities and relaxation times; absorbed into the definition of ζ_c but remains a free microphysical input.
assumptions (4)
  • domain assumption Background stars obey the Tolman–Oppenheimer–Volkoff equations for a cold barotropic fluid.
    Sec. III.A; standard equilibrium assumption for cold non-rotating stars.
  • domain assumption Perturbations are linear, purely radial, and the exterior is Schwarzschild.
    Sec. III.B; excludes non-radial couplings, nonlinear mode interactions, and heat conduction.
  • domain assumption First-order gradient expansion (Eckart or BDNK) is a valid description of the dissipative stress-energy tensor.
    Sec. II; the paper monitors frame robustness but does not prove the truncation remains valid at the largest viscosities studied.
  • standard math Causality inequalities (10) and positivity of transport coefficients guarantee well-posed linear propagation.
    Derived from characteristics of the Einstein–BDNK system; standard within the BDNK literature.

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Pith. "Pith review of Radial Oscillations of Viscous Stars." pith.science (2026). https://pith.science/paper/AGICBWK7

@misc{pith2026260323622,
  author       = {Pith},
  title        = {Pith review of: Radial Oscillations of Viscous Stars},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AGICBWK7}},
  note         = {Machine review of arXiv:2603.23622}
}
abstract

Oscillation modes of neutron stars, a key target for third-generation gravitational wave detectors, encode key information about their constituent nuclear matter. In this work, we study the effect of viscosity on oscillations of cold, polytropic, spherically symmetric neutron stars. We focus on purely radial oscillations and work perturbatively to linear order within two hydrodynamic frameworks: the acausal covariant generalization of the Navier-Stokes equations proposed by Eckart, and the causal generalization formulated by Bemfica, Disconzi, Noronha, and Kovtun (BDNK). We find that viscosity damps the radial modes on millisecond timescales and induces fractional shifts in the oscillation frequency which increase both with the compactness and viscosity of the star, reaching up to the percent level for the fundamental mode with bulk viscosities $\zeta\sim10^{30}\mathrm{g}/\mathrm{cm}/\mathrm{s}$. For more viscous stars, the oscillation frequency decreases, becoming zero (i.e., an overdamped mode) for $\zeta\gtrsim10^{31}\mathrm{g}/\mathrm{cm}/\mathrm{s}$. We also study the linear threshold of gravitational collapse. Consistent with recent analytic results in the zero heat conductivity limit, we find that viscosity in Eckart theory cannot stabilize an unstable inviscid star. We provide numerical evidence that viscosity in BDNK theory is similarly unable to prevent gravitational collapse, but it slightly modifies the threshold of collapse. Overall, our results advance our understanding of the impact of viscosity on the oscillation modes of neutron stars, a key component of viscous asteroseismology with next-generation gravitational wave detectors.

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Reference graph

Works this paper leans on

69 extracted references · 36 linked inside Pith · cited by 3 Pith papers

  1. [1]

    Perfect Fluid and Eckart Frame In the Eckart and perfect fluid cases, it is helpful to in- troduce the Lagrangian displacementξ, whereδu=∂ �ξ. This allows one to solve thettandtrEinstein equations to obtain δλ=−8πrξ(p+ϵ)e � ,(14a) δϵ=− 1 r2 d dr � r2ξ(p+ϵ) � .(14b) TherrEinstein equation can be solved for∂ �δν, which, alongside (14), can be substituted in...

  2. [2]

    Causal Frames The additional terms in the BDNK stress-energy ten- sor increase the order of the highest derivatives in the problem and complicate the structure of the lower-order Einstein equations. As a result, introducing the La- 6 grangian displacement no longer permits a direct time- integration of thetrEinstein equation, which, in the Eckart case, al...

  3. [3]

    Eckart Frame Regularity of solutions to the master equation (15) at the center of the star requiresξ(0) = 0and ˙ξ(t,0) =

  4. [4]

    In all our simulations, we choose our initial data to be stationary, i.e.,˙ξ(0, r) = 0

    We integrate the master equation forward in time from initial dataξ(0, r)and ˙ξ(0, r)using an RK4time integrator. In all our simulations, we choose our initial data to be stationary, i.e.,˙ξ(0, r) = 0

  5. [5]

    turns on

    Causal Frames We have found direct numerical integration of the sys- tem (19) to be prone to numerical instabilities. In par- ticular, we attempted to numerically integrate (19) in time using an explicit RK4scheme. We found that the resulting discretized solutions generally blow up at the boundaries of the spatial domain much faster than the dynamical tim...

  6. [6]

    From hadrons to quarks in neutron stars: a review,

    Gordon Baym, Tetsuo Hatsuda, Toru Kojo, Philip D. Powell, Yifan Song, and Tatsuyuki Takatsuka, “From hadrons to quarks in neutron stars: a review,” Rept. Prog. Phys.81, 056902 (2018), arXiv:1707.04966 [astro- ph.HE]

    arXiv 2018

  7. [7]

    The Equa- tion of State of Hot, Dense Matter and Neutron Stars,

    James M. Lattimer and Madappa Prakash, “The Equa- tion of State of Hot, Dense Matter and Neutron Stars,” Phys. Rept.621, 127–164 (2016), arXiv:1512.07820 [astro-ph.SR]

    arXiv 2016

  8. [8]

    Heavy Ion Collisions: The Big Picture, and the Big Questions,

    Wit Busza, Krishna Rajagopal, and Wilke van der Schee, “Heavy Ion Collisions: The Big Picture, and the Big Questions,” Ann. Rev. Nucl. Part. Sci.68, 339–376 (2018), arXiv:1802.04801 [hep-ph]

    arXiv 2018

Show all 69 references
  1. [9]

    Color superconductivity in dense quark matter,

    Mark G. Alford, Andreas Schmitt, Krishna Rajagopal, and Thomas Schäfer, “Color superconductivity in dense quark matter,” Rev. Mod. Phys.80, 1455–1515 (2008), arXiv:0709.4635 [hep-ph]

    2008 arXiv

  2. [10]

    GW170817: Observation of Gravitational Waves from a Binary Neu- tron Star Inspiral,

    B. P. Abbottet al.(LIGO Scientific, Virgo), “GW170817: Observation of Gravitational Waves from a Binary Neu- tron Star Inspiral,” Phys. Rev. Lett.119, 161101 (2017), arXiv:1710.05832 [gr-qc]

    2017 arXiv

  3. [11]

    Proper- ties of the binary neutron star merger GW170817,

    B. P. Abbottet al.(LIGO Scientific, Virgo), “Proper- ties of the binary neutron star merger GW170817,” Phys. Rev. X9, 011001 (2019), arXiv:1805.11579 [gr-qc]

    2019 arXiv

  4. [12]

    Science Case for the Ein- stein Telescope,

    Michele Maggioreet al.(ET), “Science Case for the Ein- stein Telescope,” JCAP03, 050 (2020), arXiv:1912.02622 [astro-ph.CO]

    2020 arXiv

  5. [13]

    The Science of the Einstein Telescope,

    Adrian Abacet al.(ET), “The Science of the Einstein Telescope,” (2025), arXiv:2503.12263 [gr-qc]

    2025 arXiv

  6. [14]

    Cosmic Explorer: The U.S. Contri- butiontoGravitational-WaveAstronomybeyondLIGO,

    David Reitzeet al., “Cosmic Explorer: The U.S. Contri- butiontoGravitational-WaveAstronomybeyondLIGO,” Bull. Am. Astron. Soc.51, 035 (2019), arXiv:1907.04833 [astro-ph.IM]

    2019 arXiv

  7. [15]

    Towards gravi- tational wave asteroseismology,

    Nils Andersson and Kostas D. Kokkotas, “Towards gravi- tational wave asteroseismology,” Mon. Not. Roy. Astron. Soc.299, 1059–1068 (1998), arXiv:gr-qc/9711088

    1998 arXiv

  8. [16]

    Quasinor- mal modes of stars and black holes,

    Kostas D. Kokkotas and Bernd G. Schmidt, “Quasinor- mal modes of stars and black holes,” Living Rev. Rel.2, 2 (1999), arXiv:gr-qc/9909058

    1999 arXiv

  9. [17]

    Gravitational wave asteroseismology revisited,

    Omar Benhar, Valeria Ferrari, and Leonardo Gualtieri, “Gravitational wave asteroseismology revisited,” Phys. Rev. D70, 124015 (2004), arXiv:astro-ph/0407529

    2004 arXiv

  10. [18]

    The effect of viscosity on neutron star oscillations,

    Curt Cutler and Lee Lindblom, “The effect of viscosity on neutron star oscillations,” Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 314, March 1, 1987, p. 234-241. 314, 234–241 (1987)

    1987

  11. [19]

    Dampingtimesforneutronstaroscillations,

    Curt Cutler, Lee Lindblom, and Randall J Splinter, “Dampingtimesforneutronstaroscillations,” Astrophys- ical Journal, Part 1 (ISSN 0004-637X), vol. 363, Nov. 10, 1990, p. 603-611.363, 603–611 (1990)

    1990

  12. [20]

    Bulk viscosity of hot neutron-star matter and the maximum rotation rates of neutron stars,

    R. F. Sawyer, “Bulk viscosity of hot neutron-star matter and the maximum rotation rates of neutron stars,” Phys. Rev. D39, 3804–3806 (1989)

    1989

  13. [21]

    Viscous Dissipation and Heat Conduction in Binary Neutron-Star Mergers,

    Mark G. Alford, Luke Bovard, Matthias Hanauske, Lu- ciano Rezzolla, and Kai Schwenzer, “Viscous Dissipation and Heat Conduction in Binary Neutron-Star Mergers,” Phys. Rev. Lett.120, 041101 (2018), arXiv:1707.09475 [gr-qc]

    2018 arXiv

  14. [22]

    Beta equilibrium inneutronstarmergers,

    Mark G. Alford and Steven P. Harris, “Beta equilibrium inneutronstarmergers,” Phys.Rev.C98,065806(2018), arXiv:1803.00662 [nucl-th]

    2018 arXiv

  15. [23]

    Bulk Viscous Damping of Density Oscillations in Neutron Star Mergers,

    Mark Alford, Arus Harutyunyan, and Armen Se- drakian, “Bulk Viscous Damping of Density Oscillations in Neutron Star Mergers,” Particles3, 500–517 (2020), 16 arXiv:2006.07975 [nucl-th]

    2020 arXiv

  16. [24]

    Projecting the likely importance of weak- interaction-driven bulk viscosity in neutron star merg- ers,

    Elias R. Most, Steven P. Harris, Christopher Plumberg, Mark G. Alford, Jorge Noronha, Jacquelyn Noronha- Hostler, Frans Pretorius, Helvi Witek, and Nicolás Yunes, “Projecting the likely importance of weak- interaction-driven bulk viscosity in neutron star merg- ers,” Mon. Not....

    2021 arXiv

  17. [25]

    Emergence of Microphysical Bulk Viscosity in Binary Neutron Star Postmerger Dynamics,

    Elias R. Most, Alexander Haber, Steven P. Harris, Ziyuan Zhang, Mark G. Alford, and Jorge Noronha, “Emergence of Microphysical Bulk Viscosity in Binary Neutron Star Postmerger Dynamics,” Astrophys. J. Lett. 967, L14 (2024), arXiv:2207.00442 [astro-ph.HE]

    2024 arXiv

  18. [26]

    Tidal heating as a direct probe of strangeness inside neutron stars,

    Suprovo Ghosh, Bikram Keshari Pradhan, and De- barati Chatterjee, “Tidal heating as a direct probe of strangeness inside neutron stars,” Phys. Rev. D109, 103036 (2024), arXiv:2306.14737 [gr-qc]

    2024 arXiv

  19. [27]

    Tidal dissipation in binary neutron star inspirals from hyperon bulk viscosity: Phase modeling and parameter estimation bias,

    Suprovo Ghosh, Samanwaya Mukherjee, Sukanta Bose, and Debarati Chatterjee, “Tidal dissipation in binary neutron star inspirals from hyperon bulk viscosity: Phase modeling and parameter estimation bias,” Mon. Not. Roy. Astron. Soc.2987, 2996 (2025), arXiv:2503.14606 [gr-qc]

    2025

  20. [28]

    Tidal heating in binary inspiral of strange quark stars,

    Suprovo Ghosh, José Luis Hernández, Bikram Ke- shari Pradhan, Cristina Manuel, Debarati Chatterjee, and Laura Tolos, “Tidal heating in binary inspiral of strange quark stars,” Phys. Rev. D112, 084072 (2025), arXiv:2504.07659 [gr-qc]

    2025

  21. [29]

    Investigating tidal heat- ing in neutron stars via gravitational Raman scattering,

    M. V. S. Saketh, Zihan Zhou, Suprovo Ghosh, Jan Stein- hoff, and Debarati Chatterjee, “Investigating tidal heat- ing in neutron stars via gravitational Raman scattering,” Phys. Rev. D110, 103001 (2024), arXiv:2407.08327 [gr- qc]

    2024 arXiv

  22. [30]

    A constraint on the dis- sipative tidal deformability of neutron stars,

    Justin L. Ripley, Abhishek Hegade K. R., Rohit S. Chan- dramouli, and Nicolas Yunes, “A constraint on the dis- sipative tidal deformability of neutron stars,” Nature As- tron.8, 1277–1283 (2024), arXiv:2312.11659 [gr-qc]

    2024 arXiv

  23. [31]

    Probing internal dissipative processes of neutron stars with gravitational waves during the inspiral of neu- tron star binaries,

    Justin L. Ripley, Abhishek Hegade K. R., and Nicolas Yunes, “Probing internal dissipative processes of neutron stars with gravitational waves during the inspiral of neu- tron star binaries,” Phys. Rev. D108, 103037 (2023), arXiv:2306.15633 [gr-qc]

    2023 arXiv

  24. [32]

    Dynamical tidal response of nonrotating rel- ativistic stars,

    Abhishek Hegade K. R., Justin L. Ripley, and Nicolás Yunes, “Dynamical tidal response of nonrotating rel- ativistic stars,” Phys. Rev. D109, 104064 (2024), arXiv:2403.03254 [gr-qc]

    2024 arXiv

  25. [33]

    Perturbations of relativistic dis- sipative stars,

    Jaime Redondo-Yuste, “Perturbations of relativistic dis- sipative stars,” (2024), arXiv:2411.16841 [gr-qc]

    2024 arXiv

  26. [34]

    The dynamical re- sponse of viscous objects to gravitational waves,

    Valentin Boyanov, Vitor Cardoso, Kostas D. Kokko- tas, and Jaime Redondo-Yuste, “The dynamical re- sponse of viscous objects to gravitational waves,” (2024), arXiv:2411.16861 [gr-qc]

    2024 arXiv

  27. [35]

    Superradiant amplification by rotating viscous compact objects,

    Jaime Redondo-Yuste and Vitor Cardoso, “Superradiant amplification by rotating viscous compact objects,” Phys. Rev. D112, L061501 (2025), arXiv:2506.13850 [gr-qc]

    2025 arXiv

  28. [36]

    Numerical modeling of bulk viscosity in neutron stars,

    Michail Chabanov and Luciano Rezzolla, “Numerical modeling of bulk viscosity in neutron stars,” Phys. Rev. D111, 044074 (2025), arXiv:2311.13027 [gr-qc]

    2025 arXiv

  29. [37]

    ImpactofBulk Viscosity on the Postmerger Gravitational-Wave Signal from Merging Neutron Stars,

    MichailChabanovandLucianoRezzolla,“ImpactofBulk Viscosity on the Postmerger Gravitational-Wave Signal from Merging Neutron Stars,” Phys. Rev. Lett.134, 071402 (2025), arXiv:2307.10464 [gr-qc]

    2025 arXiv

  30. [38]

    Microphys- ical Aspects of Binary Neutron Star Mergers,

    Michail Chabanov, Alejandro Cruz-Osorio, Christian Ecker, Claudio Meringolo, Carlo Musolino, Luciano Rez- zolla, Samuel Tootle, and Konrad Topolski, “Microphys- ical Aspects of Binary Neutron Star Mergers,” inHigh Performance Computing in Science and Engineering ’22 (2024)

    2024

  31. [39]

    Radial oscillations of zero-temperature white dwarfs and neutron stars below nuclear densities

    G. Chanmugam, “Radial oscillations of zero-temperature white dwarfs and neutron stars below nuclear densities.” Astrophys. J.217, 799–808 (1977)

    1977

  32. [40]

    The Radial Oscillations of Neutron Stars,

    E. N. Glass and L. Lindblom, “The Radial Oscillations of Neutron Stars,” Astrophys. J.53, 93 (1983)

    1983

  33. [41]

    Radial oscil- lations of relativistic stars,

    Kostas. D. Kokkotas and Johannes Ruoff, “Radial oscil- lations of relativistic stars,” Astron. Astrophys.366, 565 (2001), arXiv:gr-qc/0011093

    2001 arXiv

  34. [42]

    Coupling of radial and axial non-radial oscillations of compact stars: Gravitational waves from first-order differential rotation,

    Andrea Passamonti, Marco Bruni, Leonardo Gualtieri, Alessandro Nagar, and Carlos F. Sopuerta, “Coupling of radial and axial non-radial oscillations of compact stars: Gravitational waves from first-order differential rotation,” Phys. Rev. D73, 084010 (2006), arXiv:gr- qc/0601001

    2006

  35. [43]

    Gravitational Waves from Nonlinear Cou- plings of Radial and Polar Nonradial Modes in Relativis- tic Stars,

    Andrea Passamonti, Nikolaos Stergioulas, and Alessan- dro Nagar, “Gravitational Waves from Nonlinear Cou- plings of Radial and Polar Nonradial Modes in Relativis- tic Stars,” Phys. Rev. D75, 084038 (2007), arXiv:gr- qc/0702099

    2007

  36. [44]

    Dynamical instability of gaseous massesapproachingtheschwarzschildlimitingeneralrel- ativity,

    S. Chandrasekhar, “Dynamical instability of gaseous massesapproachingtheschwarzschildlimitingeneralrel- ativity,” Phys. Rev. Lett.12, 114–116 (1964)

    1964

  37. [45]

    A Catalogue of Methods for Studying the Nor- mal Modes of Radial Pulsation of General-Relativistic Stellar Models,

    James M. Bardeen, Kip S. Thorne, and David W. Meltzer, “A Catalogue of Methods for Studying the Nor- mal Modes of Radial Pulsation of General-Relativistic Stellar Models,” Astrophys. J.145, 505 (1966)

    1966

  38. [46]

    Radial oscillations of viscous neutron stars: Zero diffusion case,

    Raissa F. P. Mendes, Amanda Guerrieri, João V. M. Mu- niz, Gabriel S. Rocha, and Gabriel S. Denicol, “Radial oscillations of viscous neutron stars: Zero diffusion case,” Phys. Rev. D113, 024010 (2026), arXiv:2509.12330 [gr- qc]

    2026

  39. [47]

    Causality and existence of solutions of rela- tivistic viscous fluid dynamics with gravity,

    Fábio S. Bemfica, Marcelo M. Disconzi, and Jorge Noronha, “Causality and existence of solutions of rela- tivistic viscous fluid dynamics with gravity,” Phys. Rev. D98, 104064 (2018), arXiv:1708.06255 [gr-qc]

    2018 arXiv

  40. [48]

    Causality and existence of solutions of rel- ativistic viscous fluid dynamics with gravity,

    Fábio S. Bemfica, Marcelo M. Disconzi, and Jorge Noronha, “Causality and existence of solutions of rel- ativistic viscous fluid dynamics with gravity,” Physical Review D98(2018), 10.1103/physrevd.98.104064

    2018 doi

  41. [49]

    Nonlinear Causality of General First-Order Relativistic Viscous Hydrodynamics,

    Fábio S. Bemfica, Fábio S. Bemfica, Marcelo M. Dis- conzi, Marcelo M. Disconzi, Jorge Noronha, and Jorge Noronha, “Nonlinear Causality of General First-Order Relativistic Viscous Hydrodynamics,” Phys. Rev. D 100, 104020 (2019), [Erratum: Phys.Rev.D 105, 069902 (2022)], arXiv:1...

    2019 arXiv

  42. [50]

    First-Order General-Relativistic Vis- cous Fluid Dynamics,

    Fabio S. Bemfica, Marcelo M. Disconzi, and Jorge Noronha, “First-Order General-Relativistic Vis- cous Fluid Dynamics,” Phys. Rev. X12, 021044 (2022), arXiv:2009.11388 [gr-qc]

    2022 arXiv

  43. [51]

    First-order relativistic hydrodynamics is stable,

    Pavel Kovtun, “First-order relativistic hydrodynamics is stable,” Journal of High Energy Physics2019(2019), 10.1007/jhep10(2019)034

    2019 doi

  44. [52]

    Neu- tron star evolution with BDNK viscous hydrodynamics framework,

    Harry L. H. Shum, Fernando Abalos, Yago Bea, Miguel Bezares, Pau Figueras, and Carlos Palenzuela, “Neu- tron star evolution with BDNK viscous hydrodynamics framework,” (2025), arXiv:2509.15303 [gr-qc]

    2025 arXiv

  45. [53]

    Neutron star radial perturbations for causal, viscous, relativistic flu- ids,

    Daniel A. Caballero and Nicolás Yunes, “Neutron star radial perturbations for causal, viscous, relativistic flu- ids,” Phys. Rev. D112, 063050 (2025), arXiv:2506.09149 [gr-qc]. 17

    2025

  46. [54]

    Neutron- staroscillations.jl,

    Lennox S. Keeble and Jaime Redondo-Yuste, “Neutron- staroscillations.jl,” (2026)

    2026

  47. [55]

    Lectures on hydrodynamic fluctuations in relativistic theories,

    Pavel Kovtun, “Lectures on hydrodynamic fluctuations in relativistic theories,” J. Phys. A45, 473001 (2012), arXiv:1205.5040 [hep-th]

    2012 arXiv

  48. [56]

    6 (Elsevier, 1987)

    Lev Davidovich Landau and Evgenii Mikhailovich Lif- shitz,Fluid Mechanics: Volume 6, Vol. 6 (Elsevier, 1987)

    1987

  49. [57]

    The Thermodynamics of irreversible pro- cesses. 3.. Relativistic theory of the simple fluid,

    Carl Eckart, “The Thermodynamics of irreversible pro- cesses. 3.. Relativistic theory of the simple fluid,” Phys. Rev.58, 919–924 (1940)

    1940

  50. [58]

    A form of heat-conduction equations which eliminates the paradox of instantaneous propaga- tion,

    Carlo Cattaneo, “A form of heat-conduction equations which eliminates the paradox of instantaneous propaga- tion,” Comptes rendus247, 431 (1958)

    1958

  51. [59]

    Relativistic hydrodynamics with irreversible thermodynamics without the paradox of infinite velocity of heat conduction,

    M Kranyš, “Relativistic hydrodynamics with irreversible thermodynamics without the paradox of infinite velocity of heat conduction,” Il Nuovo Cimento B (1965-1970)42, 51–70 (1966)

    1965

  52. [60]

    Stability and causality in dissipative relativistic fluids,

    W. A. Hiscock and L. Lindblom, “Stability and causality in dissipative relativistic fluids,” Annals Phys.151, 466– 496 (1983)

    1983

  53. [61]

    Generic instabil- ities in first-order dissipative relativistic fluid theories,

    William A. Hiscock and Lee Lindblom, “Generic instabil- ities in first-order dissipative relativistic fluid theories,” Phys. Rev. D31, 725–733 (1985)

    1985

  54. [62]

    Relativistic Navier-Stokes description of the quark-gluon plasma radial flow,

    Yago Bea, “Relativistic Navier-Stokes description of the quark-gluon plasma radial flow,” (2025), arXiv:2503.02931 [hep-ph]

    2025 arXiv

  55. [63]

    R. C. Tolman,Relativity, Thermodynamics, and Cosmol- ogy(1934)

    1934

  56. [64]

    Gravita- tional waves from pulsations of neutron stars described by realistic Equations of State,

    Sebastiano Bernuzzi and Alessandro Nagar, “Gravita- tional waves from pulsations of neutron stars described by realistic Equations of State,” Phys. Rev. D78, 024024 (2008), arXiv:0803.3804 [gr-qc]

    2008 arXiv

  57. [65]

    Accretion driven gravitational radiation from nonrotating compact objects. Infalling quadrupo- lar shells,

    Alessandro Nagar, Guillermo Diaz, Jose A. Pons, and Jose A. Font, “Accretion driven gravitational radiation from nonrotating compact objects. Infalling quadrupo- lar shells,” Phys. Rev. D69, 124028 (2004), arXiv:gr- qc/0403077

    2004

  58. [66]

    Kreiss and J

    H. Kreiss and J. Oliger,Methods for the Approximate So- lution of Time Dependent Problems, Global Atmospheric Research Programme (GARP): GARP Publication Se- ries, Vol. 10 (GARP Publication, Geneva, Switzerland, 1973)

    1973

  59. [67]

    The oscillations of a vis- cous liquid globe,

    Subrahmanyan Chandrasekhar, “The oscillations of a vis- cous liquid globe,” Proceedings of the London Mathemat- ical Society3, 141–149 (1959)

    1959

  60. [68]

    Non-linear radial oscillations of neutron stars,

    Michael Gabler, Ulrich Sperhake, and Nils Andersson, “Non-linear radial oscillations of neutron stars,” Phys. Rev. D80, 064012 (2009), arXiv:0906.3088 [gr-qc]

    2009 arXiv

  61. [69]

    Impact of Viscosity on Ax- ial Oscillations of Neutron Stars,

    Sofia Bussieres-Lopez, Jaime Redondo-Yuste, Jose Javier Ortega, and Vitor Cardoso, “Impact of Viscosity on Ax- ial Oscillations of Neutron Stars,” (2026). 18 Appendix A: Convergence T ests In this appendix, we present convergence tests for a subset of the time-domain simulatio...

    2026

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