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Is Relativistic Hydrodynamics always Symmetric-Hyperbolic in the Linear Regime?

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arxiv 2210.05067 v2 pith:65GIDTLZ submitted 2022-10-11 nucl-th gr-qc

Lorenzo Gavassino This is my paper · ORCID
classification nucl-thgr-qc
keywords symmetric-hyperbolicalwaysconditionsequationsequilibriumhydrodynamicslinearonsager-casimir
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Close to equilibrium, the kinetic coefficients of a thermodynamic system must satisfy a set of symmetry conditions, which follow from the Onsager-Casimir principle. Here, we show that, if a system of hydrodynamic equations is analysed from the perspective of the Onsager-Casimir principle, then it is possible to impose very strong symmetry conditions also on the principal part of such equations (the part with highest derivatives). In particular, we find that, in the absence of macroscopic magnetic fields and spins, relativistic hydrodynamics should always be symmetric-hyperbolic, when linearised about equilibrium. We use these results to prove that Carter's multifluid theory and the Israel-Stewart theory in the pressure frame are both symmetric-hyperbolic in the linear regime. Connections with the GENERIC formalism are also explored.

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Cited by 3 Pith papers

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

  1. The Lorentzian geometry of relaxation

    nucl-th 2026-07 accept novelty 8.0 of 10

    Causality forces purely relaxational dispersion relations to follow spacelike trajectories on the Lorentzian {iω,ik} plane, producing universal bounds on diffusivity, viscosity, time-dilation deviations, and hydrodyna...

  2. How Lorentz boosts reshape relaxation spectra

    gr-qc 2026-01 accept novelty 8.0 of 10

    Under an Onsager-type symmetry, boosted k=0 non-hydrodynamic relaxation rates of a relativistic fluid are bounded by a(1-v)/γ ≤ iω' ≤ b/[γ(1-v)] in terms of rest-frame bounds a,b and boost speed v.

  3. Mapping Sparse Triangular Solves to GPUs via Fine-grained Domain Decomposition

    cs.PF 2025-08 unverdicted novelty 5.0 of 10

    A domain-decomposition scheme sizes subdomains to GPU shared memory to remove synchronization from sparse triangular solves, reporting 10.7x and 3.2x speedups for triangular solves and ILU0-BiCGSTAB on the AMD MI210.

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