Israel-Stewart Formalism Research Articles

Stability and causality of rest frame modes in second-order spin hydrodynamics

We analyze the low- and high-momentum rest frame modes in the second-order spin hydrodynamics and check the asymptotic causality of the theory. A truncation scheme of the Israel-Stewart formalism derived in our earlier work is proposed that extends the minimal causal formulation. It consists of altogether 40 interconnected relaxation-type dynamical equations—16 (24) of them correspond to the independent components of the energy-momentum (spin) tensor. Similarly to previous studies, we find that the stability of the perturbations and asymptotic causality require using the spin equation of state that satisfies the generalized Frenkel condition demanding that the “electric” and “magnetic” components of the spin density tensor have opposite signs. For low-momentum modes this behavior is similar to that found earlier for the first-order (Navier-Stokes) spin hydrodynamics. Published by the American Physical Society 2024

Qualitative analysis for viscous cosmologies in a non linear regime of the Israel-Stewart formalism

We explore the dynamical properties of a cosmological model that includes viscous effects in the dark matter sector of the fluid equations in a flat Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime. The bulk viscous effects are described by a non linear extension of the full Israel-Stewart model, which is a fluid causal scheme. We allow the interchange of energy in the dark sector and describe this by means of the interaction term, namely Q. We establish the dynamical system corresponding to Friedmann and fluid set of equations associated to the model and study the linear stability of its critical points. From the exploration of the dynamical system, we show the appearance of a critical point characterizing a de Sitter universe within the non interacting and interacting dark sector. We focus our study to analyse the stability of this fixed point in a large region of parameter space and derive linearized solutions around it. These approximate and analytical solutions are potentially able to describe the expansion of the universe since they are close to a de Sitter stationary solution. Within this regime with Q ≠ 0, we realize the existence of regions in the space of parameters where this critical point is stable and describes the behavior of dark energy as quintessence, cosmological constant and phantom like fluids. We perform a comparison between numerical and linearized solutions nearby the critical points within the full non linear regimes and also contrast them against ΛCDM model as a fiducial model. We find that the fully non linear regime is favored by observations and closer to the concordance model due to the non-zero value of the parameter j, which controls the non linear effects of bulk viscosity. In fact, at low redshift values, the expansion rate associated to the full non linear regime is practically indistinguishable from the ΛCDM model. The deceleration parameter obtained in this regime exhibits a transition from decelerated to accelerated cosmic expansion.

Second order causal hydrodynamics in Eckart frame: using gradient expansion scheme

In the present work, we develop a causal theory of relativistic non-ideal fluids up to the second order in the Eckart frame using gradient expansion scheme. Keeping the spirit of Mueller–Israel–Stewart formalism, the general forms of bulk viscosity, shear viscosity tensor and the heat flow vector are presented. Since each of the flux quantities explicitly carry curvature terms, we show that our formalism finds application in astrophysics in particular in the strong gravity regime. We elucidate two such applications namely in viscous thick accretion disks also known as Polish doughnuts and in addressing non-rotating equilibrium configuration, like neutron stars.

Dynamics of non-adiabatic charged spherical gravitational collapse in [formula omitted] gravity

In current manuscript, we have analyzed the effects of charge on non-adiabatic gravitational collapse dynamics in the framework of f(R,T) gravity utilizing Misner-Sharp approach. The modified field equations of f(R,T) gravity have been evaluated for the spherically symmetric sphere spacetime. The deviation of total energy inside the spacetime of the gravitating compact object has been determined by Misner and Sharp mass function. The key role of some important factors appeared in dynamical equation are investigated in detail. The Bianchi identities affected by electromagnetic field are formulated in f(R,T) gravity to find dynamical equation for compact object. Furthermore, we coupled the causal heat transport equation obtained in the context of Mu¨ller-Israel-Stewart formalism with dynamical equation. To see the more physical results, we have applied a linear model of f(R,T) gravity. Also we have investigated the impacts of matter-curvature coupling constant λ on gravitational forces and inertial mass density. It diminishes the significance of the gravitational force which result to slow down the collapse rate. The proposed applications which are directly related to astrophysical scenarios have been widely discussed.

Cosmological and thermodynamics consequences of viscous modified theories of gravity

The illustration of cosmic acceleration is being presented in the framework of DGP braneworld and dynamical Chern–Simons modified gravity in the presence of casual Israel–Stewart formalism. In this way, we discuss the evolution parameter which leads to the accelerated expansion of the universe in the phantom as well as quintessence region for both gravities. The squared speed of sound [Formula: see text] leads to the stable behavior of the current physical system in both gravities in the later epoch. Also, the entropy variation, as well as thermal equilibrium condition, remains valid in both frameworks at the present and later epoch.

Dynamics of non-adiabatic gravitating compact object in f(R, T) gravity

In this paper, we have discussed the dynamics of non-adiabatic gravitating compact object in f(R, T) theory using the Misner–Sharp approach. Here, we have extended the work of Herrera and Santos, to the modified f(R, T) theory of gravity. In order to discuss the effects of heat flux on the dynamics of compact object, we have taken the non-adiabatic source inside spherically symmetric compact object and modified field equations have been evaluated in f(R, T) gravity. The Misner–Sharp mass has been used to discuss the variation of total energy inside the gravitating compact object. The dynamical equations have been formulated by using the Bianchi identities in f(R, T) gravity. Further, the dynamical equations have been coupled with the heat transportation equation resulting from the framework of Mu¨ller–Israel–Stewart formalism. To analyze the results deeper, we have used the functional form of f(R, T) model, for such model the matter-curvature coupling constant λ has some direct effects on inertial mass density and gravitational forces. It makes the gravitational force less active thereby reducing the rate of collapse.

Dynamics of Dissipative Viscous Cylindrical Collapse with Full Causal Approach in f(R) Gravity

The idea of this article is to examine the effects on dynamics of dissipative gravitational collapse in nonstatic cylindrical symmetric geometry by using Misner-Sharp concept in framework of metric f(R) gravity theory. In this interest, we extended our study to the dissipative dark source case in both forms of heat flow and the free radiation streaming. Moreover, the role of different quantities such as heat flux, bulk, and shear viscosity in the dynamical equation is evaluated in thorough version. The dynamical equation is then coupled with full causal transportation equations in the context of Israel-Stewart formalism. The present scheme explains the physical consequences of the gravitational collapse and that is given in the decreasing form of inertial mass density which depends on thermodynamics viscous/heat coupling factors in background of f(R) theory of gravity. It is very interesting to tell us that the motives of this theory are reproduced for f(R)=R into general theory of relativity that has been done earlier.

Dynamics of viscous cosmologies in the full Israel-Stewart formalism

A detailed dynamical analysis for a bulk viscosity model in the full Israel-Stewart formalism for a spatially flat Friedmann-Robertson-Walker universe is performed. In our study we have considered the total cosmic fluid constituted by radiation, dark matter, and dark energy. The dark matter fluid is treated as an imperfect fluid which has a bulk viscosity that depends on its energy density in the usual form $\ensuremath{\xi}({\ensuremath{\rho}}_{m})={\ensuremath{\xi}}_{0}{\ensuremath{\rho}}_{m}^{1/2}$, whereas the other components are assumed to behave as perfect fluids with constant equation of state parameter. We show that the thermal history of the Universe is reproduced provided that the viscous coefficient satisfies the condition ${\ensuremath{\xi}}_{0}\ensuremath{\ll}1$, either for a zero or a suitable nonzero coupling between dark energy and viscous dark matter. In this case, the final attractor is a dark-energy-dominated, accelerating universe, with an effective equation of state parameter in the quintessence-like, cosmological constant-like, or phantom-like regime, in agreement with observations. As our main result, we show that in order to obtain a viable cosmological evolution and at the same time alleviating the cosmological coincidence problem via the mechanism of scaling solution, an explicit interaction between dark energy and viscous dark matter seems inevitable. This result is consistent with the well-known fact that models where dark matter and dark energy interact with each other have been proposed to solve the coincidence problem. Furthermore, by insisting on above, we show that in the present context a phantom nature of this interacting dark energy fluid is also favored.

Gravitational waves from remnant massive neutron stars of binary neutron star merger: Viscous hydrodynamics effects

Employing a simplified version of the Israel-Stewart formalism of general-relativistic shear-viscous hydrodynamics, we explore the evolution of a remnant massive neutron star of binary neutron star merger and pay special attention to the resulting gravitational waveforms. We find that for the plausible values of the so-called viscous alpha parameter of the order ${10}^{\ensuremath{-}2}$ the degree of the differential rotation in the remnant massive neutron star is significantly reduced in the viscous time scale, $\ensuremath{\lesssim}5\text{ }\text{ }\mathrm{ms}$. Associated with this, the degree of nonaxisymmetric deformation is also reduced quickly, and as a consequence, the amplitude of quasiperiodic gravitational waves emitted also decays in the viscous time scale. Our results indicate that for modeling the evolution of the merger remnants of binary neutron stars we would have to take into account magnetohydrodynamics effects, which in nature could provide the viscous effects.

General relativistic viscous hydrodynamics of differentially rotating neutron stars

Employing a simplified version of the Israel-Stewart formalism for general-relativistic shear-viscous hydrodynamics, we perform axisymmetric general-relativistic simulations for a rotating neutron star surrounded by a massive torus, which can be formed from differentially rotating stars. We show that with our choice of a shear-viscous hydrodynamics formalism, the simulations can be stably performed for a long time scale. We also demonstrate that with a possibly high shear-viscous coefficient, not only viscous angular momentum transport works but also an outflow could be driven from a hot envelope around the neutron star for a time scale $\ensuremath{\gtrsim}100\text{ }\text{ }\mathrm{ms}$ with the ejecta mass $\ensuremath{\gtrsim}{10}^{\ensuremath{-}2}\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$, which is comparable to the typical mass for dynamical ejecta of binary neutron-star mergers. This suggests that massive neutron stars surrounded by a massive torus, which are typical outcomes formed after the merger of binary neutron stars, could be the dominant source for providing neutron-rich ejecta, if the effective shear viscosity is sufficiently high, i.e., if the viscous $\ensuremath{\alpha}$ parameter is $\ensuremath{\gtrsim}{10}^{\ensuremath{-}2}$. The present numerical result indicates the importance of a future high-resolution magnetohydrodynamics simulation that is the unique approach to clarify the viscous effect in the merger remnants of binary neutron stars by the first-principle manner.

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.

Crossing the phantom divide with dissipative normal matter in the Israel–Stewart formalism

A phantom solution in the framework of the causal Israel-Stewart (IS) formalism is discussed. We assume a late time behavior of the cosmic evolution by considering only one dominant matter fluid with viscosity. In the model it is assumed a bulk viscosity of the form $\xi= \xi_{0}\rho^{1/2}$, where $\rho$ is the energy density of the fluid. We evaluate and discuss the behavior of the thermodynamical parameters associated to this solution, like the temperature, rate of entropy, entropy, relaxation time, effective pressure and effective EoS. A discussion about the assumption of near equilibrium of the formalism and the accelerated expansion of the solution is presented. 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 time independent. A future singularity (big rip) occurs, but different from the Type I (big rip) solution classified in S. Nojiri, S. D. Odintsov and S. Tsujikawa, Phys. Rev. D 71, 063004 (2005), if we consider others thermodynamics parameters like, for example, the effective pressure in the presence of viscosity or the relaxation time.

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.

Causal viscous hydrodynamics in 2 + 1 dimensions for relativistic heavy-ion collisions

We explore the effects of shear viscosity on the hydrodynamic evolution and final hadron spectra of Cu + Cu collisions at ultrarelativistic collision energies, using the newly developed (2 + 1)-dimensional viscous hydrodynamic code VISH2+1. Based on the causal Israel-Stewart formalism, this code describes the transverse evolution of longitudinally boost-invariant systems without azimuthal symmetry around the beam direction. Shear viscosity is shown to decelerate the longitudinal and accelerate the transverse hydrodynamic expansion. For fixed initial conditions, this leads to a longer quark-gluon plasma (QGP) lifetime, larger radial flow in the final state, and flatter transverse momentum spectra for the emitted hadrons compared to ideal fluid dynamic simulations. We find that the elliptic flow coefficient ${v}_{2}$ is particularly sensitive to shear viscosity: even the lowest value allowed by the AdS/CFT conjecture $\ensuremath{\eta}/s\ensuremath{\geqslant}1/4\ensuremath{\pi}$ suppresses ${v}_{2}$ enough to have significant consequences for the phenomenology of heavy-ion collisions at the BNL Relativistic Heavy Ion Collider (RHIC). A comparison between our numerical results and earlier analytic estimates of viscous effects within a blast-wave model parametrization of the expanding fireball at freeze-out reveals that the full dynamical theory leads to much tighter constraints for the specific shear viscosity $\ensuremath{\eta}/s$, thereby supporting the notion that the quark-gluon plasma created at RHIC exhibits almost ``perfect fluidity.''

Entropy current in conformal hydrodynamics

In recent work [1, 2], the energy-momentum tensor for the = 4 SYM fluid was computed up to second derivative terms using holographic methods. The aim of this note is to propose an entropy current (accurate up to second derivative terms) consistent with this energy-momentum tensor and to explicate its relation with the existing theories of relativistic hydrodynamics. In order to achieve this, we first develop a Weyl-covariant formalism which simplifies the study of conformal hydrodynamics. This naturally leads us to a proposal for the entropy current of an arbitrary conformal fluid in any spacetime (with d>3). In particular, this proposal translates into a definite expression for the entropy flux in the case of = 4 SYM fluid. We conclude this note by comparing the formalism presented here with the conventional Israel-Stewart formalism.

Dissipative generalized Chaplygin gas as phantom dark energy

Abstract The generalized Chaplygin gas, characterized by the equation of state p = − A / ρ α , has been considered as a model for dark energy due to its dark-energy-like evolution at late times. When dissipative processes are taken into account, within the framework of the standard Eckart theory of relativistic irreversible thermodynamics, cosmological analytical solutions are found. Using the truncated causal version of the Israel–Stewart formalism, a suitable model was constructed which crosses the w = − 1 barrier. The future-singularities encountered in both approaches are of a new type, and not included in the classification presented by Nojiri and Odintsov [S. Nojiri, S.D. Odintsov, Phys. Rev. D 72 (2005) 023003].