Extending Israel and Stewart hydrodynamics to relativistic superfluids via Carter's multifluid approach

Gavassino, Lorenzo; Antonelli, Marco; Haskell, Brynmor

doi:10.48550/arxiv.2110.05546

Cited by 1 publication

(6 citation statements)

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“…Note that, if some currents are superfluid, we can define some quasi-conserved topological charges (i.e. winding numbers [6]), whose existence is responsible for the long life of the superflow [26,37]. However, in the present paper, we will assume that such quasi-conservation laws are eventually broken at the length/time-scales of interest (and we will not includes such charges among the "Q I ").…”

Section: B Allowed Processesmentioning

confidence: 99%

“…In this section, we provide a quick overview of Carter's multifluid theory using the generating function approach [26]. Then, we apply the Gibbs stability criterion [27] in the "fluid + environment" formulation [29].…”

Section: Setting the Stagementioning

confidence: 99%

“…The central postulate of the theory is that the fluxes of the multifluid are determined by the following differential [26]:…”

Section: A Carter's Theorymentioning

confidence: 99%

“…A one-component superfluid, such as 4 He, can be modelled, in the non-dissipative limit [26], as a multifluid with two currents: s a (entropy current), and n a (conserved particle current). The resulting theory is the relativistic generalization of Landau's two-fluid model for superfluidity 7 [41].…”

Section: Relativistic Two-fluid Model For Superfluid Heliummentioning

confidence: 99%

“…Hence, one is forced to rely on approximations, e.g. by setting some entrainment coefficients to zero [26]. But we do not know, in general, if an approximation of this kind is permitted, or if it spoils the reliability of the whole theory.The goal of this paper is to finally derive the stability and causality conditions of Carter's multifluid theory.…”

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confidence: 99%

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Stability and causality of Carter's multifluid theory

Gavassino¹

2022

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Stability and causality are studied for linear perturbations about equilibrium in Carter's multifluid theory. Our stability analysis is grounded on the requirement that the entropy of the multifluid, plus that of the environment, must be maximised at equilibrium. This allows us to compute a quadratic Lyapunov functional, whose positive definiteness implies stability. Furthermore, we verify explicitly that, also for multifluids, thermodynamic stability implies linear causality. As a notable stability condition, we find that the entrainment matrix must always be positive definite, confirming a widespread intuition. I. INTRODUCTIONCarter's multifluid theory [1][2][3] is the hydrodynamic framework currently adopted for modelling superfluid-normal mixtures in full general relativity [4][5][6]. It extends the notion of perfect fluid to interacting systems in which nondiffusive relative flows can survive over hydrodynamic time-scales. As such, it finds application in neutron star physics [7][8][9]: dense hadronic matter is believed to be a mixture of several chemical components, some of which are superfluid (free to spin at different rates [10][11][12]). Furthermore, the ability to describe non-diffusive out-of-equilibrium fluxes makes Carter's theory well suited for modelling dissipation beyond Fick's law [13][14][15], elevating the formalism to a pillar of Relativistic Extended Irreversible Thermodynamics [16][17][18].Despite the relevance of Carter's multifluid approach, both for non-equilibrium statistical mechanics and for astrophysical modelling, very little is known about its mathematical properties. In particular, to date no systematic study of its stability and causality properties has ever been carried out. In other words, we do not know under which conditions the initial value formulation of Carter's theory is reliable, and produces physically meaningful solutions. Only few specific hydrodynamic models, built using Carter's approach, have been shown to be reliable (or non-reliable [19]). This has always been done by invoking some mathematical correspondence [20] with the Israel-Stewart theory [21], whose stability-causality properties are well known [22]. Unfortunately, such correspondence is limited to theories with only two currents (entropy and particles), and cannot be extended to, e.g., neutron star hydrodynamics (which requires at least three currents: entropy, protons, and neutrons). This is a serious issue, not only because we do not know if the currently adopted multifluid models are reliable, but also because we have no idea of which factors contribute to make a theory stable, and which approximations, instead, may be harmful. The case of Carter's "regular theory" for heat conduction is emblematic: Carter correctly identified the origin of the instability of the theories of Eckart [23] and Landau and Lifshitz [24]; he formulated a new theory with the precise goal of fixing such pathologies [13]; nevertheless, the resulting theory turned out to be still unstable (for some realistic equations of state...

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Section: B Allowed Processesmentioning

confidence: 99%