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arxiv: 2509.15303 · v2 · submitted 2025-09-18 · 🌀 gr-qc · astro-ph.HE· nucl-th

Neutron star evolution with the Bemfica-Disconzi-Noronha-Kovtun viscous hydrodynamics framework

Harry L. H. Shum , Fernando Abalos , Yago Bea , Miguel Bezares , Pau Figueras , Carlos Palenzuela This is my paper

Pith reviewed 2026-05-18 15:39 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.HEnucl-th
keywords neutron starsviscous hydrodynamicsBDNK formulationquasi-normal modesCowling approximationnumerical simulationsrelativistic fluidsspherical symmetry
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The pith

The BDNK formulation allows stable nonlinear simulations of spherically symmetric neutron stars in a restricted parameter space under the Cowling approximation.

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

This paper demonstrates the first nonlinear numerical simulations of neutron stars using the recently proposed BDNK viscous relativistic hydrodynamics. The authors evolve spherically symmetric models with a simplified equation of state and find that stable solutions exist only within a narrow range of parameters. They then extract the frequencies of quasi-normal modes from the simulations and measure how quickly the fundamental mode decays. If these results hold, the BDNK approach could become a practical tool for modeling dissipative effects in compact objects without losing causality or stability. A sympathetic reader would care because neutron stars in real astrophysical events like mergers involve out-of-equilibrium fluid dynamics that standard perfect-fluid models ignore.

Core claim

The authors carry out the first nonlinear simulations of spherically symmetric neutron stars in the BDNK first-order viscous hydrodynamics framework, employing the Cowling approximation and a simple equation of state. They identify a restricted region of the parameter space where the evolutions remain stable over the simulated timescales. Within these stable runs they compute the spectrum of quasi-normal modes and determine the damping time of the lowest-frequency mode, establishing a baseline for viscous neutron-star dynamics.

What carries the argument

The BDNK formulation of causal, stable, first-order relativistic viscous hydrodynamics, implemented numerically in spherical symmetry with the Cowling approximation.

If this is right

  • Viscous effects can be included in neutron star models without violating causality.
  • Quasi-normal mode frequencies and decay rates depend on the viscous parameters in BDNK.
  • Numerical stability requires careful choice of viscosity coefficients and relaxation times.
  • This framework can serve as a foundation for more complex, non-spherical simulations.

Where Pith is reading between the lines

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

  • Extending these simulations beyond the Cowling approximation might reveal gravitational wave signatures modified by viscosity.
  • The restricted parameter space could correspond to physical regimes in hot or dense matter where relaxation times are short.
  • Comparing the computed mode decay rates to those from other viscous formulations would test the robustness of the results.

Load-bearing premise

That the BDNK viscous hydrodynamics remains numerically stable and physically meaningful for neutron star matter when evolved in spherical symmetry under the Cowling approximation with the selected simplified equation of state and limited parameter choices.

What would settle it

Running a simulation with parameters outside the reported stable range that develops exponential growth or unphysical oscillations within the simulated time, or finding that the extracted mode frequencies do not match expected values from linear perturbation theory in the zero-viscosity limit.

Figures

Figures reproduced from arXiv: 2509.15303 by Carlos Palenzuela, Fernando Abalos, Harry L. H. Shum, Miguel Bezares, Pau Figueras, Yago Bea.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p011_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p014_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p018_6.png] view at source ↗
read the original abstract

The recently proposed first-order viscous relativistic hydrodynamics formulation by Bemfica, Disconzi, Noronha, and Kovtun (commonly known as the BDNK formulation) has been shown to be causal, stable, strongly hyperbolic, and thus locally well-posed. It is now a viable new option for modelling out-of-equilibrium effects in fluids, and has attracted wide attention in its potential applications to astrophysical systems. In this work, we present the first non-linear numerical simulation of spherically symmetric neutron stars using the BDNK formulation under the Cowling approximation. Using a simplified equation of state, we show that stable evolutions can be constructed within a restricted parameter space up to the simulation time we explored. From these simulations, we analyse the frequency content of the quasi-normal modes and the decay rate of the fundamental mode. This analysis serves as a first step towards constructing a fully consistent model of neutron stars using the BDNK formulation.

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

3 major / 2 minor

Summary. The paper presents the first non-linear numerical simulation of spherically symmetric neutron stars using the BDNK viscous hydrodynamics formulation under the Cowling approximation. With a simplified equation of state, it reports that stable evolutions can be obtained within a restricted range of the BDNK viscosity and relaxation parameters up to the explored simulation times, followed by an analysis of the frequency content of quasi-normal modes and the decay rate of the fundamental mode.

Significance. If the reported stability and mode extraction hold beyond the narrow parameter window and simplified EOS, this would constitute a valuable first demonstration that the BDNK framework can be applied to dynamical neutron-star spacetimes. The work supplies concrete numerical evidence of long-term stability and extractable QNM signals in a controlled setting, which is a necessary prerequisite for future extensions to realistic transport coefficients and equations of state.

major comments (3)
  1. [Results] Results section (and abstract): The manuscript achieves stable evolutions only after restricting the BDNK viscosity coefficients and relaxation times to a narrow interval chosen to suppress instabilities. No mapping is provided between this interval and the ranges allowed by nuclear-physics bounds on shear and bulk viscosity in neutron-star matter; without such a demonstration the claim that BDNK is a viable framework for neutron-star modeling rests on an untested assumption.
  2. [§3] Numerical methods / §3: The paper asserts stable evolutions and extracts QNM frequencies and decay rates, yet supplies no description of the discretization scheme, grid resolution, artificial viscosity or damping parameters, convergence tests, or error estimates. These omissions make it impossible to assess whether the reported stability and mode properties are numerically robust or sensitive to resolution.
  3. [§4] §4 (mode analysis): The quasi-normal-mode frequencies and fundamental-mode decay rates are obtained with a simplified polytropic or similar EOS. The manuscript does not discuss how these quantities would shift under a more realistic, density-dependent equation of state that includes finite-temperature or composition effects, which are known to alter both the background structure and the viscous damping rates.
minor comments (2)
  1. [Abstract] The abstract states that the evolutions are performed “up to the simulation time we explored”; a quantitative statement of the maximum evolution time in units of the dynamical timescale would help readers gauge the practical stability.
  2. Notation for the BDNK transport coefficients (e.g., the relaxation times τ_π, τ_Π and viscosity coefficients η, ζ) should be defined explicitly at first use and kept consistent with the original BDNK literature.

Simulated Author's Rebuttal

3 responses · 2 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. The points raised are helpful for clarifying the scope and limitations of this first exploratory study. We address each major comment below, indicating where revisions will be made.

read point-by-point responses

  1. Referee: [Results] Results section (and abstract): The manuscript achieves stable evolutions only after restricting the BDNK viscosity coefficients and relaxation times to a narrow interval chosen to suppress instabilities. No mapping is provided between this interval and the ranges allowed by nuclear-physics bounds on shear and bulk viscosity in neutron-star matter; without such a demonstration the claim that BDNK is a viable framework for neutron-star modeling rests on an untested assumption.

    Authors: We agree that the explored parameter space is deliberately restricted to achieve stable evolutions within the current numerical implementation and simplified setup. This is explicitly noted in the manuscript as a controlled first step. We will revise the abstract and results section to state more clearly that the interval is selected for numerical stability rather than to represent specific physical values. We will also add a short discussion acknowledging that a direct mapping to nuclear-physics bounds on shear and bulk viscosity requires separate microphysical modeling and lies outside the present scope. This revision will temper the claim while preserving the demonstration that stable evolutions are possible in a restricted but non-trivial region of parameter space. revision: partial

  2. Referee: [§3] Numerical methods / §3: The paper asserts stable evolutions and extracts QNM frequencies and decay rates, yet supplies no description of the discretization scheme, grid resolution, artificial viscosity or damping parameters, convergence tests, or error estimates. These omissions make it impossible to assess whether the reported stability and mode properties are numerically robust or sensitive to resolution.

    Authors: We acknowledge this omission in the description of the numerical methods. We will expand §3 to include the specific discretization scheme (finite-difference order and stencil), the grid resolutions employed, any artificial viscosity or damping parameters introduced for stability, and the results of convergence tests together with error estimates on the extracted frequencies and decay rates. These additions will allow readers to evaluate the numerical robustness of the reported stability and mode properties. revision: yes

  3. Referee: [§4] §4 (mode analysis): The quasi-normal-mode frequencies and fundamental-mode decay rates are obtained with a simplified polytropic or similar EOS. The manuscript does not discuss how these quantities would shift under a more realistic, density-dependent equation of state that includes finite-temperature or composition effects, which are known to alter both the background structure and the viscous damping rates.

    Authors: The choice of a simplified polytropic EOS was made to isolate the implementation and stability properties of the BDNK formulation. We agree that realistic EOS effects are important. We will add a paragraph in §4 that qualitatively discusses how density-dependent EOS with finite-temperature and composition effects are expected to modify the stellar structure, sound speeds, QNM frequencies, and viscous damping rates, citing relevant literature on neutron-star oscillations. We will emphasize that quantitative shifts require future work with advanced EOS implementations and that the present results serve as a baseline demonstration. revision: partial

standing simulated objections not resolved
  • A quantitative mapping of the restricted BDNK parameter interval to nuclear-physics bounds on viscosity coefficients in neutron-star matter.
  • Full numerical simulations and quantitative mode analysis performed with realistic, density-dependent equations of state that incorporate finite-temperature and composition effects.

Circularity Check

0 steps flagged

No significant circularity in numerical simulation results

full rationale

The manuscript reports the first nonlinear numerical evolutions of spherically symmetric neutron stars in the BDNK formulation under the Cowling approximation. Results (stable evolution in a restricted parameter window, extracted QNM frequencies, and fundamental-mode decay rates) are obtained by direct time integration of the hydrodynamic equations with a simplified EOS. No derivation chain is claimed that reduces by construction to fitted inputs, self-defined quantities, or a self-citation load-bearing uniqueness theorem. The BDNK framework itself is cited from independent prior work by different authors and is treated as an external input. The restriction to a narrow parameter space to achieve stability is an empirical numerical finding, not a logical reduction to the paper's own assumptions. The work is therefore self-contained against external benchmarks and receives the default non-circularity score.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the prior theoretical properties of the BDNK formulation and on the numerical stability achieved only after restricting parameters and using a simplified equation of state.

free parameters (1)
  • BDNK viscosity and relaxation parameters
    The abstract states that stable evolutions exist only within a restricted parameter space, indicating these coefficients are selected or tuned to maintain stability.
axioms (1)
  • domain assumption The BDNK formulation is causal, stable, and strongly hyperbolic.
    Invoked as established in prior work and taken as given for the numerical application.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

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