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arxiv: 2606.20957 · v1 · pith:PYB3WHQCnew · submitted 2026-06-18 · 🌀 gr-qc · astro-ph.HE

Out-of-Equilibrium Effects in Non-Radial Relativistic Stellar Perturbations: A Model-Agnostic Formulation and Mode Analysis

Takuya Katagiri , Victor Guedes , Kent Yagi This is my paper

Pith reviewed 2026-06-26 15:56 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.HE
keywords relativistic stellar perturbationsnon-radial oscillationsnonequilibrium effectsviscositythermal conductivityLindblom-Detweiler formalismeven parityodd parity
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The pith

A model-agnostic framework extends the Lindblom-Detweiler formalism to incorporate generic nonequilibrium corrections into non-radial relativistic stellar perturbations in both even- and odd-parity channels.

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

The paper builds the first general framework for linear non-radial perturbations of relativistic stars that includes out-of-equilibrium effects such as viscosity and thermal conductivity. It extends the Lindblom-Detweiler equations using only the tensorial structure and thermodynamic decomposition of the corrections, without assuming any specific constitutive relations. This structural approach shows how the corrections modify the equations for geometric deformations and fluid fluctuations. The framework is then applied to the Bemfica-Disconzi-Noronha-Kovtun fluid to compute perturbative shifts in mode frequencies and damping times, while also identifying features that can produce extra mode families.

Core claim

The central claim is the construction of a unified, model-agnostic framework for non-radial relativistic stellar perturbations that incorporates generic nonequilibrium corrections to the perfect-fluid sector in both even- and odd-parity channels. The framework is formulated in terms of the tensorial structure and thermodynamic decomposition of the corrections, without relying on any specific constitutive relations. This decomposition determines how the effects enter the perturbation equations and contribute to geometric deformations and fluid fluctuations. Application to the Bemfica-Disconzi-Noronha-Kovtun fluid yields perturbative shifts in frequencies and damping times of modes connected t

What carries the argument

Extension of the Lindblom-Detweiler formalism via the tensorial structure and thermodynamic decomposition of generic nonequilibrium corrections to the perfect-fluid sector.

If this is right

  • Nonequilibrium corrections enter the perturbation equations and contribute to geometric deformations and fluid fluctuations through the tensorial and thermodynamic decomposition.
  • For the Bemfica-Disconzi-Noronha-Kovtun fluid, modes connected to perfect-fluid counterparts exhibit shifts in frequencies and damping times when transport coefficients vanish perturbatively.
  • Structural features of the closed eigenvalue problem can produce additional mode families beyond those of the perfect-fluid case.
  • The same unified framework applies to any relativistic fluid theory to determine how it modifies the structure of non-radial stellar perturbations.

Where Pith is reading between the lines

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

  • Observed frequencies of stellar oscillations could be used to place bounds on the size of nonequilibrium corrections inside neutron stars.
  • The decomposition method could be applied to rotating or magnetized stars by adding the corresponding background terms to the same equations.
  • Similar tensorial decompositions might organize out-of-equilibrium effects in perturbations of other compact objects, such as black-hole accretion flows.

Load-bearing premise

The tensorial structure and thermodynamic decomposition of generic nonequilibrium corrections can be introduced into the Lindblom-Detweiler equations without relying on any specific constitutive relations.

What would settle it

Direct numerical solution of the perturbation equations for a specific viscous fluid using both the general decomposition and the full constitutive relations, checking whether the mode frequencies and damping times agree exactly in the small-coefficient limit.

Figures

Figures reproduced from arXiv: 2606.20957 by Kent Yagi, Takuya Katagiri, Victor Guedes.

Figure 1
Figure 1. Figure 1: The quadrupolar (ℓ = 2) f-mode shifts induced by shear viscosity (left panel) and bulk viscosity (right panel) with the phenomenological coefficients in Eq. (92) and the rest-mass polytropic equation of state in Eq. (93) for a fixed stellar compactness of M/R ≃ 0.1460. The black cross denotes the f-mode frequency and the damping time of the perfect-fluid case, (fPF, τPF) ≃ (1.578 × 103Hz, 2.934 × 10−1 s). … view at source ↗
Figure 2
Figure 2. Figure 2: Absolute values of the relative shifts of the [PITH_FULL_IMAGE:figures/full_fig_p014_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The quadrupolar (ℓ = 2) even-parity w-mode shifts induced by shear viscosity (left panel) and bulk viscosity (right panel). Note the opposite sign of the horizontal axis of the right panel. The black cross denotes the w-mode frequency and the damping time for the perfect-fluid case, (fPF, τPF) ≃ (1.009 × 105Hz, 2.264 × 10−5 s). The equation of state and stellar compactness are the same as in [PITH_FULL_IM… view at source ↗
Figure 4
Figure 4. Figure 4: Absolute values of the relative shifts of the [PITH_FULL_IMAGE:figures/full_fig_p015_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The quadrupolar (ℓ = 2) odd-parity w-mode shifts (left panel) and the corresponding absolute values of the relative shifts with respect to the perfect-fluid case (right panel). Here, we define ∆f = f − fPF and ∆τ = τ − τPF. The black cross denotes the odd-parity w-mode frequency and the damping time for the perfect-fluid case, (fPF, τPF) ≃ (7.088×103Hz, 2.815× 10−5 s). The equation of state and stellar com… view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of our perturbative results with the [PITH_FULL_IMAGE:figures/full_fig_p016_6.png] view at source ↗
read the original abstract

We present a systematic, model-agnostic analysis of out-of-equilibrium effects, including viscosity and thermal conductivity, in non-radial oscillations of relativistic stars. Extending the Lindblom-Detweiler formalism, we construct, to our knowledge, the first general framework for linear, non-radial relativistic stellar perturbations that incorporates generic nonequilibrium corrections to the perfect-fluid sector in both the even- and odd-parity channels. Our framework is formulated in terms of the tensorial structure and thermodynamic decomposition of generic corrections without relying on any specific constitutive relations, thereby allowing us to elucidate, at a structural level, how these effects enter the perturbation equations and contribute to geometric deformations and fluid fluctuations. As an application, we consider the Bemfica-Disconzi-Noronha-Kovtun fluid and perturbatively investigate shifts in the frequencies and damping times of modes connected to their perfect-fluid counterparts in the limit of vanishing transport coefficients. We also identify structural features of the closed eigenvalue problem that can give rise to additional mode families. Our formalism provides a unified framework for analyzing how different relativistic fluid theories modify the structure of non-radial stellar perturbations.

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 / 3 minor

Summary. The paper presents a systematic, model-agnostic analysis of out-of-equilibrium effects, including viscosity and thermal conductivity, in non-radial oscillations of relativistic stars. Extending the Lindblom-Detweiler formalism, it constructs a general framework for linear, non-radial relativistic stellar perturbations that incorporates generic nonequilibrium corrections to the perfect-fluid sector in both even- and odd-parity channels. The framework is formulated in terms of the tensorial structure and thermodynamic decomposition of generic corrections without relying on specific constitutive relations. As an application, it perturbatively investigates shifts in the frequencies and damping times of modes for the Bemfica-Disconzi-Noronha-Kovtun (BDNK) fluid in the limit of vanishing transport coefficients and identifies structural features of the closed eigenvalue problem that can give rise to additional mode families.

Significance. If the structural decomposition closes the eigenvalue problem as claimed, this provides a unified framework for analyzing how different relativistic fluid theories with dissipation modify non-radial stellar perturbations. This is significant for modeling dissipative effects in neutron star dynamics and their potential gravitational-wave signatures, with the model-agnostic approach allowing broad applicability across fluid models.

major comments (2)
  1. [§3] §3 (framework construction): the assertion that the tensorial structure and thermodynamic decomposition of generic corrections can be introduced into the Lindblom-Detweiler equations without specific constitutive relations, and that this decomposition is sufficient to close the eigenvalue problem for both parity sectors, requires explicit verification. The manuscript should display the resulting perturbation equations and confirm that the number of independent equations matches the number of variables after decomposition.
  2. [§5] §5 (BDNK application): the perturbative calculation of frequency and damping-time shifts must explicitly demonstrate recovery of the perfect-fluid Lindblom-Detweiler modes in the vanishing-transport-coefficient limit, including the first-order correction terms and confirmation that no spurious modes are introduced at this order.
minor comments (3)
  1. The introduction should expand the literature review to include additional references on dissipative effects in relativistic stellar perturbations to better support the novelty claim.
  2. Notation for the correction tensors and thermodynamic variables should be collected in a dedicated table or appendix for clarity when comparing to the original Lindblom-Detweiler variables.
  3. Figure captions describing mode shifts would benefit from additional detail on the parameter values used and the scale of the plotted quantities.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and for identifying points that will improve the clarity of the manuscript. We address each major comment below. The revisions will consist of adding explicit equation displays and verification steps without altering the core claims of the work.

read point-by-point responses

  1. Referee: §3 (framework construction): the assertion that the tensorial structure and thermodynamic decomposition of generic corrections can be introduced into the Lindblom-Detweiler equations without specific constitutive relations, and that this decomposition is sufficient to close the eigenvalue problem for both parity sectors, requires explicit verification. The manuscript should display the resulting perturbation equations and confirm that the number of independent equations matches the number of variables after decomposition.

    Authors: We agree that explicit verification strengthens the presentation. In the revised version we will display the complete set of linearized perturbation equations for both even- and odd-parity sectors after the thermodynamic decomposition is substituted. We will then tabulate the number of independent equations and unknowns (including the auxiliary variables introduced by the generic corrections) to confirm that the system remains closed and that the eigenvalue problem is well-posed. This count follows directly from the fact that the decomposition respects the original Lindblom-Detweiler variable structure while adding only the dissipative contributions consistent with the thermodynamic relations already used in the perfect-fluid sector. revision: yes

  2. Referee: §5 (BDNK application): the perturbative calculation of frequency and damping-time shifts must explicitly demonstrate recovery of the perfect-fluid Lindblom-Detweiler modes in the vanishing-transport-coefficient limit, including the first-order correction terms and confirmation that no spurious modes are introduced at this order.

    Authors: The perturbative expansion is constructed so that the zeroth-order equations are identically the Lindblom-Detweiler system; this is stated in the manuscript but not written out in full detail. In revision we will explicitly substitute the vanishing-transport-coefficient limit into the first-order correction equations, recover the original modes, and display the resulting first-order shifts in frequency and damping time. We will also note that the perturbative ordering preserves the number of degrees of freedom, thereby excluding spurious modes at this order. The BDNK constitutive relations enter only through the first-order source terms and do not enlarge the variable set. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper constructs a model-agnostic extension of the Lindblom-Detweiler equations by inserting the tensorial structure and thermodynamic decomposition of generic nonequilibrium corrections into both parity sectors. This is done without invoking specific constitutive relations or fitting any parameters to data within the paper; the subsequent perturbative application to the BDNK fluid is an explicit limit-taking exercise on an external fluid model. No derivation step reduces by construction to a self-definition, a fitted input relabeled as a prediction, or a load-bearing self-citation chain. The central result is therefore an independent structural generalization whose content is not equivalent to its own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central construction rests on the assumption that a tensorial and thermodynamic decomposition of nonequilibrium corrections exists and can be inserted into the Lindblom-Detweiler equations without further specification; no free parameters or invented entities are mentioned in the abstract.

axioms (1)
  • domain assumption The Lindblom-Detweiler formalism admits a systematic insertion of generic nonequilibrium corrections via their tensorial structure and thermodynamic decomposition.
    This premise is invoked to justify the model-agnostic construction of the perturbation equations.

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discussion (0)

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Reference graph

Works this paper leans on

106 extracted references · 35 linked inside Pith

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    To this end, we perform a harmonic decomposition for metric and fluid perturbations

    Nonequilibrium amplitudes Here, we introduce fundamental variables associated withS µν andJ µ, and collectively call themnonequi- librium amplitudes. To this end, we perform a harmonic decomposition for metric and fluid perturbations. In the Regge-Wheeler gauge [84], the metric perturbation in the Fourier domain reads δgµνdxµdxν =−r ℓ H ℓmeνdt2 −2iωrH ℓm ...

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    Small-transport-coefficient expansion We work within a small-transport-coefficient expan- sion. In other words, we introduce a bookkeeping param- eter in front of the transport coefficients, and expand the perturbation variables in terms of it. The assumption for the small transport coefficients is commonly adopted in previous work [78, 86] and is support...

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    Structural suppression of the causal-regulator corrections Equations (64) and (65) show that the contributions associated withτ E andτ P enter through the same com- bination, implying that they affect the perturbation in a similar manner. As presented in Eqs. (B1), (B4), and (B7), the contributions ofτ E andτ p enterS 00,S 0, andS Ω, and are proportional ...

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