Israel-Stewart Theory Research Articles

Testing a Nonlinear Solution of the Israel–Stewart Theory

Testing a Nonlinear Solution of the Israel–Stewart Theory

Matter–curvature effects upon the dissipative viscous collapse of massive stellar object

This paper investigates the evolutionary phases of a collapsing dissipative star cluster in the presence of dark matter. For this purpose, the minimal coupling model of [Formula: see text] gravity is used as a candidate for exotic matter in star cluster. The collapse equation is derived from generalized dynamical equations which show the total conservation of energy within the cluster. In this context, the approach of Misner and Sharp is applied to study the phenomenon and differentiate between homologous as well as non-homologous gravitational collapse. The generalized dynamical equations are also connected to modified heat transport equations related to heat flux, viscosity and shear, which deals with Israel–Stewart theory (without removing the thermodynamics heat/viscous coupling coefficients). It is found that shear-free and non-dissipative fluid give homologous collapse. The dissipation of collapsing star cluster provides a relation between tidal forces and density inhomogeneity. It is theoretically predicted that the presence of exotic matter controlled the collapsing mechanism.

Symmetry-based study and dynamics of casual bulk viscous matter-dominated universe

The dynamics of cosmological expansion is studied for a spatially flat matter-dominated universe filled with barotropic casual bulk viscous fluid. The evolution equation for the Hubble parameter is derived using Friedmann equations and conservation law for the viscous fluid, in which the viscous pressure is modeled by truncated version of the full Israel-Stewart theory of bulk viscosity. We use a Lie symmetry-based approach to study the evolution of the expansion rate of the Universe. The model equation possesses eight-parameter Lie symmetry generators and gives two different analytic group invariant solutions for the Hubble parameter. Expressions for various important cosmological parameters are obtained and values are estimated analytically for the explanation of the evolution dynamics of the Universe. The interesting features of the obtained symmetry-based solutions are that, one satisfies the present acceleration of the Universe, while the other could not support present accelerating phase, rather represents a universe dominated by non-viscous stiff fluid. We make useful checks on the observational constraints on the model parameters from the latest released observational data. The accelerating phase of the current universe is investigated using observational bounds and compared the model under investigation with the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}CDM model. The evolutionary cosmic phases obtained from the analysis of the Lie symmetry-based solutions correspond to the association with the critical points in the equivalent phase space. These interesting features are investigated and analyzed using dynamical systems approach.

Correlation of density fluctuation in a magnetized QCD matter near the critical end point

The dynamical correlation of density fluctuation in quark gluon plasma with a critical end point has been investigated within the scope of the Müller–Israel–Stewart theory in the presence of static ultra-high external magnetic field. The dynamic structure factor of the density fluctuation exhibits three Lorentzian peaks in absence of external magnetic field – a central Rayleigh peak and two Brillouin peaks situated symmetrically on the opposite sides of the Rayleigh peak. The spectral structure displays five peaks in presence of the magnetic field due to the coupling of the magnetic field with the hydrodynamic fields in second-order hydrodynamics. The emergence of the extra peaks is due to the asymmetry in the pressure gradient caused by the external magnetic field in the system. Interestingly, it is observed that near the critical end point, all the Brillouin peaks disappear irrespective of the presence or absence of the external magnetic field.

Late time cosmological solutions in f(R,T) gravity in a viscous universe

Considering the condition on conservation of energy–momentum tensor (EMT), we study late time cosmological solutions in the context of [Formula: see text] gravity (where [Formula: see text] and n are constants) in a flat Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime. The present model discusses the case of a barotropic perfect fluid as the matter content of the Universe, along with the case when dissipative effects are taken into account. Briefly, assuming a single perfect fluid, we find that the mentioned model is not capable of presenting an observationally consistent picture of the late time accelerated expansion of the Universe; nevertheless, the model leads to admissible solutions when the bulk viscosity is included. In this regard, a consistent setting is found considering the Eckart, Truncated and Full Israel–Stewart theories which determine the behavior of bulk viscosity. In the presence of bulk viscosity, the behavior of the deceleration parameter (DP) shows that the underlying model can describe an acceptable evolution even if the isotropic pressure of matter content of the Universe is negligible.

Relativistic bulk viscous fluids of Burgers type and their presence in neutron stars

It is well known that a mixture of two chemical components undergoing one chemical reaction is a bulk viscous fluid, where the bulk stress evolves according to the Israel-Stewart theory. Here, we show that a mixture of three independent chemical components undergoing two distinct chemical reactions can also be viewed as a bulk viscous fluid, whose bulk stress now is governed by a second-order differential equation which reproduces the Burgers model for viscoelasticity. This is a rigorous and physically motivated example of a fluid model where the viscous stress does not undergo simple Maxwell-Cattaneo relaxation, and can actually overshoot the Navier–Stokes stress. We show that, if one accounts for muons, neutron star matter is indeed a bulk viscous fluid of Burgers type.

Linear stability analysis of Israel-Stewart theory in the case of a nonzero background charge

Linear stability analysis of Israel-Stewart theory in the case of a nonzero background charge

Is relativistic hydrodynamics always symmetric-hyperbolic in the linear regime?

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 analyzed 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 linearized 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.

Relativistic liquids: GENERIC or EIT?

We study the GENERIC hydrodynamic theory for relativistic liquids formulated by Öttinger and collaborators. We use the maximum entropy principle to derive its conditions for linear stability (in an arbitrary reference frame) and for relativistic causality. In addition, we show that, in the linear regime, its field equations can be recast into a symmetric-hyperbolic form. Once rewritten in this way, the linearised field equations turn out to be a particular realisation of the Israel–Stewart theory, where some of the Israel–Stewart free parameters are constrained. This also allows us to reinterpret the GENERIC framework in view of the principles of extended irreversible thermodynamics and to discuss its physical relevance to model (possibly viscoelastic) fluids.

Phenomenological Relativistic Second-Order Hydrodynamics for Multiflavor Fluids

In this work, we perform a phenomenological derivation of the first- and second-order relativistic hydrodynamics of dissipative fluids. To set the stage, we start with a review of the ideal relativistic hydrodynamics from energy–momentum and particle number conservation equations. We then go on to discuss the matching conditions to local thermodynamical equilibrium, symmetries of the energy–momentum tensor, decomposition of dissipative processes according to their Lorentz structure, and, finally, the definition of the fluid velocity in the Landau and Eckart frames. With this preparatory work, we first formulate the first-order (Navier–Stokes) relativistic hydrodynamics from the entropy flow equation, keeping only the first-order gradients of thermodynamical forces. A generalized form of diffusion terms is found with a matrix of diffusion coefficients describing the relative diffusion between various flavors. The procedure of finding the dissipative terms is then extended to the second order to obtain the most general form of dissipative function for multiflavor systems up to the second order in dissipative fluxes. The dissipative function now includes in addition to the usual second-order transport coefficients of Israel–Stewart theory also second-order diffusion between different flavors. The relaxation-type equations of second-order hydrodynamics are found from the requirement of positivity of the dissipation function, which features the finite relaxation times of various dissipative processes that guarantee the causality and stability of the fluid dynamics. These equations contain a complete set of nonlinear terms in the thermodynamic gradients and dissipative fluxes arising from the entropy current, which are not present in the conventional Israel–Stewart theory.

Dark energy density and Israel–Stewart (IS) bulk viscosity model

In this paper, we investigate the thermodynamics of a dark energy bulk viscosity model as a cosmic fluid. In this regard, the two theories of Eckart and Israel–Stewart (IS) are the bases of our work. Therefore, we first investigate the thermodynamics of cosmic fluids in the dark energy bulk viscosity model and the general relationships. Then, we express the thermodynamic relationships of Eckart’s theory. Due to the basic equations of Eckart’s theory and Friedmann’s equations, we consider two states, one is [Formula: see text] (standard) and the other is [Formula: see text] (non-standard). In the standard state, we define the pressure [Formula: see text], energy density [Formula: see text] and bulk viscosity coefficient [Formula: see text] of the cosmic fluid in terms of cosmic time and we obtain its relations. We also mention that in this standard state, because of [Formula: see text], the value of [Formula: see text] is zero, so [Formula: see text] is not defined in this state. But in the non-standard case [Formula: see text], the bulk viscosity coefficient [Formula: see text] is zero and only the scale factor, pressure and energy density of the cosmic fluid are defined. We also consider two states of constant and variable bulk viscosity coefficients and obtain three Hubble constant parameters and scale factor in terms of cosmic time, and energy density in terms of scale factor. In the state of variable bulk viscosity coefficient, we consider the viscosity coefficient as the power law from energy density [Formula: see text], which is [Formula: see text] and a constant. Following this, we discuss about the dissipative effects of cosmic fluids and examine the effects of energy density for dark energy in the IS theory. The results are comprehensively presented in Tables 1 and 2. Also, according to observational constraints, the results of the likelihood analysis for the IS viscous model are summarized in Table 3.

Symmetric-hyperbolic quasihydrodynamics

We set up a general framework for systematically building and classifying, in the linear regime, causal and stable dissipative hydrodynamic theories that, alongside with the usual hydrodynamic modes, also allow for an arbitrary number of nonhydrodynamic modes with complex dispersion relation (such theories are often referred to as ``quasihydrodynamic''). To increase the number of nonhydrodynamic modes, one needs to add more effective fields to the model. The system of equations governing this class of quasihydrodynamic theories is symmetric hyperbolic, thermodynamically consistent (i.e., the entropy is a Lyapunov function) and can be derived from an action principle. As a first application of the formalism, we prove that, in the linear regime, the Israel-Stewart theory in the Eckart frame and the Israel-Stewart theory in the Landau frame are exactly the same theory. In addition, with an Onsager-Casimir analysis, we show that in strongly coupled plasmas the nonequilibrium degrees of freedom typically appear in pairs, whose members acquire opposite phase under time reversal. We use this insight to modify Cattaneo's model for diffusion, in a way to make its initial transient consistent with the transient dynamics of holographic plasmas.

On high-order numerical schemes for viscous relativistic hydrodynamics through the Kelvin–Helmholtz instability

ABSTRACT This work assesses the dissipative properties of high-order numerical methods for relativistic hydrodynamics. A causal theory of physical dissipation is included within a finite volume high-resolution shock-capturing framework based on the Israel–Stewart theory to study high-order WENO (weighted-essentially non-oscillatory) schemes for simulating the relativistic Kelvin–Helmholtz instability. We provide an estimation of the numerical dissipation of high-order schemes based on results obtained both with and without physically resolved dissipation and determine an empirical relationship between the numerical dissipation and the grid resolution. We consider the appearance of secondary flow features within the evolution of the Kelvin–Helmholtz instability and determine that they are numerical artifacts — this is partly based on arguments presented in terms of a frame-dependent form of the relativistic Reynolds number. There is a potential advantage of using high-order schemes in terms of their accuracy and computational cost on coarser grid resolutions when directly compared to low-order schemes on a fine grid in the presence of physical viscosity. It is possible to find reasonable agreement between numerical results that employ lower-order schemes using a finer grid resolution and results that employ higher order schemes at a coarser grid resolution when sufficient viscosity is present. Overall, the present analysis gives an insight into the numerical dissipation of high-order shock-wave capturing schemes which can be relevant to computational studies of astrophysical phenomena in the relativistic regime. The results presented herein are problem and scheme-dependent and serve to highlight the different roles of numerical and physical dissipation.

Contrasting the bulk viscous model with the standard $\Lambda$CDM using Bayesian statistics

The causal dissipative model is a plausible choice to explain the late accelerated epoch of the universe. At the same time, \(\Lambda\)CDM is considered the standard model to explain the cosmological data corresponding to the late evolution of the universe. We consider a bulk viscous model in which dissipation is driven by the bulk viscosity \(\zeta =\alpha \rho ^{1/2}\), described using the full causal Israel-Stewart theory. We computed the model parameters using the latest observational data (Pantheon). We contrasted this model with \(\Lambda\)CDM model for the late accelerated phase using the Bayesian inference method. The Bayes factor was obtained by calculating the likelihood for Pantheon data. Suitable prior values were assumed for model parameters to calculate the likelihood. It shows that the evidence for \(\Lambda\)CDM against this viscous model is very strong according to the Jeffreys scale.

Godunov variables and convex entropy for relativistic fluid dynamics with bulk viscosity

Based on the conservation–dissipation formalism proposed by Zhu et al. [J. Non-Equilib. Thermodyn. 40, 67 (2015)], we formulate a general version of the Israel–Stewart theory for relativistic fluid dynamics with bulk viscosity. Our generalization consists in allowing for a wide range of dependence of the entropy density on the bulk viscosity. We show the existence of Godunov–Boillat variables for this model. By known properties of systems possessing such variables, this provides an alternative proof of the recently established existence of solutions for the Israel–Stewart theory locally in time, and a proof that entropy production is positive across weak Lax shocks.

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

We construct a relativistic model for bulk viscosity and heat conduction in a superfluid. Building on the principles of Unified Extended Irreversible Thermodynamics, the model is derived from Carter's multifluid approach for a theory with 3 four-currents: particles, entropy, and quasi-particles. Dissipation arises directly from the fact that the quasi-particle four-current is an independent degree of freedom that does not necessarily comove with the entropy. For small deviations from local thermodynamic equilibrium, the model provides an extension of the Israel-Stewart theory to superfluid systems. It can, therefore, be made hyperbolic, causal and stable if the microscopic input is accurate. The non-dissipative limit of the model is the relativistic two-fluid model of Carter, Khalatnikov and Gusakov. The Newtonian limit of the model is an Extended-Irreversible-Thermodynamic extension of Landau's two-fluid model. The model predicts the existence of four bulk viscosity coefficients and accounts for their microscopic origin, providing their exact formulas in terms of the quasi-particle creation rate. Furthermore, when fast oscillations of small amplitude around the equilibrium are considered, the relaxation-time term in the telegraph-type equations for the bulk viscosities accounts directly for their expected dependence on the frequency.

Exact solutions of a causal viscous FRW cosmology within the Israel–Stewart theory through factorization

Exact solutions of a causal viscous FRW cosmology within the Israel–Stewart theory through factorization

Linearized dispersion relations in viscous relativistic hydrodynamics

We compute the dispersion relations for scalar, vector and tensor modes of a viscous relativistic fluid, linearized around an equilibrium solution, for a divergence type theory (which, in the linearized theory, includes Israel-Stewart theory and anisotropic hydrodynamics as particular cases) and contrast them to the corresponding results derived from kinetic theory under the relaxation time approximation, and from causal first order theories. We conclude that all approaches give similar dynamics for the scalar and vector modes, while the particular divergence type theory presented here also contains propagating damped tensor waves, in agreement with kinetic theory. Nonhydrodynamic tensor modes are also a feature of holographic fluids. These results support the application of hydrodynamics in problems involving the interaction between fluids and gravitational waves.

On the feasibility of truncated Israel–Stewart model in the context of late acceleration

A dissipative model of the Universe based on the causal relativistic truncated Israel–Stewart theory is analysed in the context of recent accelerated expansion of the Universe. The bulk viscosity and relaxation time are taken as ξ = αρ s and respectively. For s = 1/2, we found an analytical solution for the Hubble parameter of the model. We have estimated the model parameters by treating γ = 1 and γ as a free parameter using the latest cosmological data. The model predicts a prior decelerated phase and an end de Sitter phase as in the standard ΛCDM model. The dynamical system analysis shows that the prior decelerated epoch is an unstable equilibrium, while the far future de Sitter epoch is stable. The age of the Universe obtained around 13.66 Gyr, which is close to the recent observations. The second law of thermodynamics is found to be satisfied throughout the evolution in this model. The feasibility of the model has been checked by contrasting with models based on the full Israel–Stewart and the Eckart viscous theories. The truncated viscous model appears more compatible with astronomical observations than the Eckart and full causal viscous models.

Unified Extended Irreversible Thermodynamics and the Stability of Relativistic Theories for Dissipation

In a relativistic context, the main purpose of Extended Irreversible Thermodynamics (EIT) is to generalize the principles of non-equilibrium thermodynamics to the domain of fluid dynamics. In particular, the theory aims at modeling any diffusion-type process (like heat as diffusion of energy, viscosity as diffusion of momentum, charge-conductivity as diffusion of particles) directly from thermodynamic laws. Although in Newtonian physics this task can be achieved with a first-order approach to dissipation (i.e. Navier–Stokes–Fourier like equations), in a relativistic framework the relativity of simultaneity poses serious challenges to the first-order methodology, originating instabilities which are, instead, naturally eliminated within EIT. The first part of this work is dedicated to reviewing the most recent progress made in understanding the mathematical origin of this instability problem. In the second part, we present the formalism that arises by promoting non-equilibrium thermodynamics to a classical effective field theory. We call this approach Unified Extended Irreversible Thermodynamics (UEIT), because it contains, as particular cases, EIT itself, in particular the Israel-Stewart theory and the divergence-type theories, plus Carter’s approach and most branches of non-equilibrium thermodynamics, such as relativistic chemistry and radiation hydrodynamics. We use this formalism to explain why all these theories are stable by construction (provided that the microscopic input is correct), showing that their (Lyapunov) stability is a direct consequence of the second law of thermodynamics.