Israel-Stewart Theory Research Articles

Viscous cosmologies

We probe into universes filled with quark gluon plasma with non-zero viscosities. In particular, we study the evolution of a universe with non-zero shear viscosity motivated by the theoretical result of a non-vanishing shear viscosity in the quark gluon plasma due to quantum-mechanical effects. We first review the consequences of a non-zero bulk viscosity and show explicitly the non-singular nature of the bulk-viscosity-universe by calculating the cosmological scale factor which goes to zero only asymptotically. The cosmological model with bulk viscosity is extended to include a cosmological constant. The previous results are contrasted with the cosmology with non-zero shear viscosity. We first clarify under which conditions shear viscosity terms are compatible with the Friedmann–Lamaître–Robertson–Walker metric. To this end we use a version of the energy–momentum tensor from the Müller–Israel–Stewart theory which leads to causal Navier–Stoke equations. We then derive the corresponding Friedmann equations and show under which conditions the universe emerges to be non-singular.

Nonlinear viscous cosmological models in f(R,T) gravity

This article presents nonlinear viscous cosmological model of the universe that arises in the modified gravity theory in which the Lagrangian of the gravitational action contains a general function [Formula: see text], where [Formula: see text] and [Formula: see text] denote the curvature scalar and the trace of the energy–momentum tensor, respectively, in the flat Friedmann-Robertson-Walker background metric with isotropic fluid. We obtain cosmological solutions in [Formula: see text] theory of gravity, specially for the choice [Formula: see text] with nonlinear viscosity described by nonlinear Israel Stewart theory. The physical and geometrical properties of the models in [Formula: see text] gravity, where [Formula: see text] and [Formula: see text] are coupling parameters, with nonlinear Israel Stewart theory are studied in detail. The analysis of the variation of bulk viscous pressure, energy density, scale factor, Hubble parameter and deceleration parameter with cosmic evolution is done in the nonlinear Israel Stewart theory with [Formula: see text] gravity. The stability analysis of the equilibrium points of the dynamical system associated with the exponential evolution of the universe in [Formula: see text] gravity theory with nonlinear dissipative effects is also studied.

Observational constraints on emergent universe model with non-linear viscous fluid

A flat emergent universe (EU) with a non-linear equation of state ( $$p=A \rho +f(\rho )$$ ) is studied considering bulk viscosity. In the paper we obtain cosmological models with viscous fluid described by truncated Israel–Stewart theory. Using autonomous system of field equations the stability of the solutions are analyzed. The observational constraints on the model parameters are determined for different matter energy compositions of the universe with non-linear viscosity in the EU scenario.

Dynamics of viscous dissipative collapse with casual approach in string inspired Gauss–Bonnet gravity

In this work, we have studied the effects of dissipative viscous/heat gravitational collapse on the dynamics of collapsing source in 5D Einstein–Gauss–Bonnet theory using full casual approach. For this purpose, the dynamical equations have been formulated by using Misner–Sharp approach in 5D Einstein–Gauss–Bonnet theory of gravity. Using the Müller–Israel–Stewart theory, the dynamical equations have coupled with casual transport equations for the heat flux, the bulk and shear bulk viscosity to determine the effects of heat flux including thermodynamics viscous/heat coupling coefficients. The applications of this work to certain astrophysical situations are discussed.

Bulk viscous cosmological model in f(R,T) theory of gravity

In this paper, we have presented bulk viscous cosmological model of the universe in the modified gravity theory in which the Lagragian of the gravitational action contains a general function [Formula: see text], where [Formula: see text] and [Formula: see text] denote the curvature scalar and the trace of the energy–momentum tensor, respectively, in the framework of a flat Friedmann–Robertson–Walker model with isotropic fluid. We obtain cosmological solution in [Formula: see text] theory of gravity, specially of particular choice [Formula: see text], where [Formula: see text] is a constant, in the presence of bulk viscosity that are permitted in Eckart theory, Truncated Israel Stewart (TIS) theory and Full Israel Stewart (FIS) theory. The physical and geometrical properties of the models in Eckart, TIS theory and FIS theory are studied in detail. The analysis of the variation of bulk viscous pressure, energy density, scale factor, Hubble parameter and deceleration parameter with cosmic evolution is done in the respective theories. The models are analyzed by comparison with recent observational data. The cosmological models are compatible with observations.

Analysing dissipative effects in the ΛCDM model

In the present paper, the effects of viscous dark matter are analysed within the ΛCDM model. Here we consider bulk viscosity through the Israel-Stewart theory approach, leading to an effective pressure term in the continuity equation that accomplishes for the dissipative effects of the dark matter fluid. Then, the corresponding equation for viscosity is solved and a general equation for the Hubble parameter is obtained with the presence of a cosmological constant. The existence of de Sitter solutions is discussed, where a wider range of solutions is found in comparison to the ΛCDM model. Also the conditions for the near thermodynamical equilibrium of the fluid is analysed. Finally, a qualitative analysis provides some constraints on the model by using Supernovae Ia data which reveals the possible importance of causal thermodynamics in cosmology.

Dynamics of the dissipative gravitational collapse in Einstein-Gauss-Bonnet gravity

In this work, we have investigated the effects of dissipation on the dynamics of a collapsing sphere with heat flux in 5-dimensional Einstein-Gauss-Bonnet gravity. For this purpose, the field equations as well as mass function have been formulated in the 5-dimensional Einstein-Gauss-Bonnet theory of gravity. The Misner-Sharp approach has been implemented to derive the dynamical equations in the form of proper time and radial derivatives in 5-dimensional Einstein-Gauss-Bonnet gravity. We have explored the impact of heat flux on the dynamical collapse of a spherical source. In the context of the Israel-Stewart theory, the heat transport equations are modeled to determine the impacts of radial heat flux with the assumption that in some approximations one may neglect the thermodynamics heat/viscous coupling coefficients. Further, the dynamical equations have been coupled withthe heat transport equation, and the consequences of such equation with the Gauss-Bonnet coupling constant $ \alpha$ have been discussed in detail.

Emergent universe model with dissipative effects

Emergent universe model is presented in general theory of relativity with isotropic fluid in addition to viscosity. We obtain cosmological solutions that permit emergent universe scenario in the presence of bulk viscosity that are described by either Eckart theory or Truncated Israel Stewart (TIS) theory. The stability of the solutions are also studied. In this case, the emergent universe (EU) model is analyzed with observational data. In the presence of viscosity, one obtains emergent universe scenario, which however is not permitted in the absence of viscosity. The EU model is compatible with cosmological observations.

Accelerated and decelerated expansion in a causal dissipative cosmology

In this work we explore a new cosmological solution for an universe filled with one dissipative fluid, described by a barotropic EoS $p = \omega \rho$, in the framework of the full Israel-Stewart theory. The form of the bulk viscosity has been assumed of the form $\xi = \xi_{0}\rho^{1/2}$. The relaxation time is taken to be a function of the EoS, the bulk viscosity and the speed of bulk viscous perturbations, $c_{b}$. The solution presents an initial singularity, where the curvature scalar diverges as the scale factor goes to zero. Depending on the values for $\omega$, $\xi_{0}$, $c_{b}$ accelerated and decelerated cosmic expansion can be obtained. In the case of accelerated expansion, the viscosity drives the effective EoS to be of quintessence type, for the single fluid with positive pressure. Nevertheless, we show that only the solution with decelerated expansion satisfies the thermodynamics conditions $dS/dt > 0$ (growth of the entropy) and $d^{2}S/dt^{2} < 0$ (convexity condition). We show that an exact stiff matter EoS is not allowed in the framework of the full causal thermodynamic approach; and in the case of a EoS very close to the stiff matter regime, we found that dissipative effects becomes negligible so the entropy remains constant. Finally, we show numerically that the solution is stable under small perturbations.

Some Bulk-Viscous Solutions in a First-Order Theory

We first motivate the study of viscosity in cosmology. Whilst most studies assume that the universe is filled with a perfect fluid, viscosity is expected to play a role, at least during some stages of the evolution of the Universe. There are several theories of viscosity. Eckart’s first-order theory was found to permit superluminal signals, and equilibrium states were found to be unstable. To solve these problems, the Israel-Stewart second-order theory was proposed. More recently, a relatively new first-order theory has appeared, which is claimed to also solve these problems.We briefly reviewthis first-order theory and present the basic field equations. Then we attempt to find homogeneous and isotropic solutions in the theory. It is noted that there do not exist stiff matter (pressure = energy density) solutions in the theory, in contrast to other theories. We then find power-law solutions without a cosmological term. Surprisingly, there do not exist simple exponential solutions, again in contrast to other theories. Finally, we present a solution with a cosmological term and make some concluding remarks.

Behaviour of charged collapsing fluids after hydrostatic equilibrium in R^n gravity

The purpose of this paper is to study the transport equation and its coupling with the Maxwell equation in the framework of R^n gravity. Using Müller–Israel–Stewart theory for the conduction of dissipative fluids, we analyze the temperature, heat flux, viscosity and thermal conductivity in the scenario of relaxation time. All these thermodynamical variables appear in the form of a single factor whose influence is discussed on the evolution of relativistic model for the heat conducting collapsing star.

Phantom solution in a non-linear Israel–Stewart theory

In this paper we present a phantom solution with a big rip singularity in a non-linear regime of the Israel–Stewart formalism. In this framework it is possible to extend this causal formalism in order to describe accelerated expansion, where assumption of near equilibrium is no longer valid. We assume a flat universe filled with a single viscous fluid ruled by a barotropic EoS, p=ωρ, which can represent a late time accelerated phase of the cosmic evolution. The solution allows to cross the phantom divide without evoking an exotic matter fluid and the effective EoS parameter is always lesser than −1 and constant in time.

Local equilibrium solutions in simple anisotropic cosmological models, as described by relativistic fluid dynamics

We test the physical relevance of the full and the truncated versions of the Israel–Stewart (IS) theory of irreversible thermodynamics in a cosmological setting. Using a dynamical systems method, we determine the asymptotic future of plane symmetric Bianchi type I spacetimes with a viscous mathematical fluid, keeping track of the magnitude of the relative dissipative fluxes, which determines the applicability of the IS theory. We consider the situations where the dissipative mechanisms of shear and bulk viscosity are involved separately and simultaneously. It is demonstrated that the only case in the given model when the fluid asymptotically approaches local thermal equilibrium, and the underlying assumptions of the IS theory are therefore not violated, is that of a dissipative fluid with vanishing bulk viscosity. The truncated IS equations for shear viscosity are found to produce solutions which manifest pathological dynamical features and, in addition, to be strongly sensitive to the choice of initial conditions. Since these features are observed already in the case of an oversimplified mathematical fluid model, we have no reason to assume that the truncation of the IS transport equations will produce relevant results for physically more realistic fluids. The possible role of bulk and shear viscosity in cosmological evolution is also discussed.

Dark matter perturbations and viscosity: A causal approach

The inclusion of dissipative effects in cosmic fluids modifies their clustering properties and could have observable effects on the formation of large scale structures. We analyse the evolution of density perturbations of cold dark matter endowed with causal bulk viscosity. The perturbative analysis is carried out in the Newtonian approximation and the bulk viscosity is described by the causal Israel-Stewart (IS) theory. In contrast to the non-causal Eckart theory, we obtain a third order evolution equation for the density contrast that depends on three free parameters. For certain parameter values, the density contrast and growth factor in IS mimic their behaviour in $\Lambda$CDM when $z \geq 1$. Interestingly, and contrary to intuition, certain sets of parameters lead to an increase of the clustering.

Israel-Stewart Approach to Viscous Dissipative Extended Holographic Ricci Dark Energy Dominated Universe

This paper reports a study on the truncated Israel-Stewart formalism for bulk viscosity using the extended holographic Ricci dark energy (EHRDE). Under the consideration that the universe is dominated by EHRDE, the evolution equation for the bulk viscous pressureΠin the framework of the truncated Israel-Stewart theory has been taken asτΠ˙+Π=-3ξH, whereτis the relaxation time andξis the bulk viscosity coefficient. Considering effective pressure as a sum of thermodynamic pressure of EHRDE and bulk viscous pressure, it has been observed that under the influence of bulk viscosity the EoS parameterwDEis behaving like phantom, that is,wDE≤-1. It has been observed that the magnitude of the effective pressurepeff=p+Πis decaying with time. We also investigated the case for a specific choice of scale factor; namely,a(t)=(t-t0)β/(1-α). For this choice we have observed that a transition from quintessence to phantom is possible for the equation of state parameter. However, theΛCDM phase is not attainable by the state-finder trajectories for this choice. Finally it has been observed that in both of the cases the generalized second law of thermodynamics is valid for the viscous EHRDE dominated universe enveloped by the apparent horizon.

On the viability of the truncated Israel–Stewart theory in cosmology

We apply the causal Israel–Stewart theory of irreversible thermodynamics to model the matter content of the Universe as a dissipative fluid with bulk and shear viscosity. Along with the full transport equations we consider their widely used truncated version. By implementing a dynamical systems approach to Bianchi type IV and V cosmological models with and without cosmological constant, we determine the future asymptotic states of such Universes and show that the truncated Israel–Stewart theory leads to solutions essentially different from the full theory. The solutions of the truncated theory may also manifest unphysical properties. Finally, we find that in the full theory shear viscosity can give a substantial rise to dissipative fluxes, driving the fluid extremely far from equilibrium, where the linear Israel–Stewart theory ceases to be valid.

AN EXTENDED MAGNETOHYDRODYNAMICS MODEL FOR RELATIVISTIC WEAKLY COLLISIONAL PLASMAS

Black holes that accrete far below the Eddington limit are believed to accrete through a geometrically thick, optically thin, rotationally supported plasma that we will refer to as a radiatively inefficient accretion flow (RIAF). RIAFs are typically collisionless in the sense that the Coulomb mean free path is large compared to $GM/c^2$, and relativistically hot near the event horizon. In this paper we develop a phenomenological model for the plasma in RIAFs, motivated by the application to sources such as Sgr A* and M87. The model is derived using Israel-Stewart theory, which considers deviations up to second order from thermal equilibrium, but modified for a magnetized plasma. This leads to thermal conduction along magnetic field lines and a difference in pressure, parallel and perpendicular to the field lines (which is equivalent to anisotrotropic viscosity). In the non-relativistic limit, our model reduces to the widely used Braginskii theory of magnetized, weakly collisional plasmas. We compare our model to the existing literature on dissipative relativistic fluids, describe the linear theory of the plasma, and elucidate the physical meaning of the free parameters in the model. We also describe limits of the model when the conduction is saturated and when the viscosity implies a large pressure anisotropy. In future work, the formalism developed in this paper will be used in numerical models of RIAFs to assess the importance of non-ideal processes for the dynamics and radiative properties of slowly accreting black holes.

Transport coefficients in second-order non-conformal viscous hydrodynamics

Based on the exact solution of Boltzmann kinetic equation in the relaxation-time approximation, the precision of the two most recent formulations of relativistic second-order non-conformal viscous hydrodynamics (14-moment approximation and causal Chapman-Enskog method), standard Israel-Stewart theory, and anisotropic hydrodynamics framework, in the simple case of one-dimensional Bjorken expansion, is tested. It is demonstrated that the failure of Israel-Stewart theory in reproducing exact solutions of the Boltzmann kinetic equation occurs due to neglecting and/or choosing wrong forms of some of the second-order transport coefficients. In particular, the importance of shear-bulk couplings in the evolution equations for dissipative quantities is shown. One finds that, in the case of the bulk viscous pressure correction, such coupling terms are as important as the corresponding first-order Navier-Stokes term and must be included in order to obtain, at least qualitative, overall agreement with the kinetic theory.

Nonlinear waves in second order conformal hydrodynamics

In this work we study wave propagation in dissipative relativistic fluids described by a simplified set of the 2nd order viscous conformal hydrodynamic equations corresponding to Israel–Stewart theory. Small amplitude waves are studied within the linearization approximation while waves with large amplitude are investigated using the reductive perturbation method, which is generalized to the case of 2nd order relativistic hydrodynamics. Our results indicate the presence of a “soliton-like” wave solution in Israel–Stewart hydrodynamics despite the presence of dissipation and relaxation effects.

Kinetic foundations of relativistic dissipative fluid dynamics

In this contribution we discuss in detail the most widespread formalisms employed to derive relativistic dissipative fluid dynamics from the Boltzmann equation: Chapman–Enskog expansion and Israel–Stewart theory. We further point out the drawbacks of each theory and explain possible ways to circumvent them. Recent developments in the derivation of fluid dynamics from the Boltzmann equation are also discussed.