The Misner and Sharp approach to the study of gravitational collapse is extended to the viscous dissipative case in, both, the streaming out and the diffusion approximations. The dynamical equation is then coupled to causal transport equations for the heat flux, the shear and the bulk viscosity, in the context of Israel--Stewart theory, without excluding the thermodynamics viscous/heat coupling coefficients. The result is compared with previous works where these later coefficients were neglected and viscosity variables were not assumed to satisfy causal transport equations. Prospective applications of this result to some astrophysical scenarios are discussed.
The aim of this paper is to investigate the dynamical aspects of charged viscous cylindrical source by using Misner approach. To this end, we have considered the more general charged dissipative fluid enclosed by the cylindrical symmetric spacetime. The dissipative nature of the source is due to the presence of dissipative variables in the stress-energy tensor. The dynamical equations resulting from such charged cylindrical dissipative source have been coupled with the causal transport equations for heat flux, shear and bulk viscosity, in the context of Israel-Steward theory. In this case, we …
Warm inflation model with bulk viscous pressure in the context of "intermediate inflation" where the cosmological scale factor expands as $a(t)=a_0\exp(At^f)$, is studied. The characteristics of this model in slow-roll approximation and in high dissipative regime are presented in two cases: 1- Dissipative parameter $Γ$ as a function of scalar field $ϕ$ and bulk viscous coefficient $ζ$ as a function of energy density $ρ$. 2- $Γ$ and $ζ$ are constant parameters. Scalar, tensor perturbations and spectral indices for this scenario are obtained. The cosmological parameters appearing in the present …
We present dynamical description of gravitational collapse in view of Misner and Sharp's formalism. Matter under consideration is a complicated fluid consistent with plane symmetry which we assume to undergo dissipation in the form of heat flow, radiation, shear and bulk viscosity. Junction conditions are studied for a general spacetime in the interior and Vaidya spacetime in the exterior regions. Dynamical equations are obtained and coupled with causal transport equations derived in context of M$\ddot{u}$ller Israel Stewart theory. The role of dissipative quantities over collapse is investiga…
The generalized Chaplygin gas, which interpolates between a high density relativistic era and a non-relativistic matter phase, is a popular dark energy candidate. We consider a generalization of the Chaplygin gas model, by assuming the presence of a bulk viscous type dissipative term in the effective thermodynamic pressure of the gas. The dissipative effects are described by using the truncated Israel-Stewart model, with the bulk viscosity coefficient and the relaxation time functions of the energy density only. The corresponding cosmological dynamics of the bulk viscous Chaplygin gas dominate…
We consider the dynamics of a viscous cosmological fluid in the generalized Randall-Sundrum model for an isotropic brane. To describe the dissipative effects we use the Israel-Hiscock-Stewart full causal thermodynamic theory. In the limiting case of a stiff cosmological fluid with pressure equal to the energy density, the general solution of the field equations can be obtained in an exact parametric form for a cosmological fluid with constant bulk viscosity and with a bulk viscosity coefficient proportional to the square root of the energy density, respectively. The obtained solutions describe…
We consider the dynamics of a causal bulk viscous cosmological fluid filled constantly decelerating Bianchi type I space-time. The matter component of the Universe is assumed to satisfy a linear barotropic equation of state and the state equation of the small temperature Boltzmann gas. The resulting cosmological models satisfy the condition of smallness of the viscous stress. The time evolution of the relaxation time, temperature, bulk viscosity coefficient and comoving entropy of the dissipative fluid is also obtained.
In this paper we have investigated an LRS Bianchi I anisotropic cosmological model of the universe by taking time varying $G$ and $Λ$ in the presence of bulk viscous fluid source described by full causal non-equilibrium thermodynamics. We obtain a cosmological constant as a decreasing function of time and for $m, n > 0$, the value of cosmological ``constant'' for this model is found to be small and positive which is supported by the results from recent supernovae observations.
The general solution of the gravitational field equations for a full causal bulk viscous stiff cosmological fluid, with bulk viscosity coefficient proportional to the energy density to the power 1/4, is obtained in the flat Friedmann-Robertson-Walker geometry. The solution describes a non-inflationary Universe, which starts its evolution from a singular state. The time variation of the scale factor, deceleration parameter, viscous pressure, viscous pressure-thermodynamic pressure ratio, comoving entropy and Ricci and Kretschmann invariants is considered in detail.
A cosmological model with variable G and Lambda is considered in the framework of Israel-Stewart-Hiscock (ISH) causal theory. Power law as well as inflationary solutions are obtained. The gravitational constant is found to increase with time.
We study the classical flat full causal bulk viscous FRW cosmological model through the factorization method. The method shows that there exists a relationship between the viscosity parameter $s$ and the parameter $γ$ entering the equations of state of the model. Also, the factorization method allows to find some new exact parametric solutions for different values of the viscous parameter $s$. Special attention is given to the well known case $s=1/2$, for which the cosmological model admits scaling symmetries. Furthermore, some exact parametric solutions for $s=1/2$ are obtained through the Li…
The renormalization group method is applied to the study of homogeneous and flat Friedmann-Robertson-Walker type Universes, filled with a causal bulk viscous cosmological fluid. The starting point of the study is the consideration of the scaling properties of the gravitational field equations, of the causal evolution equation of the bulk viscous pressure and of the equations of state. The requirement of scale invariance imposes strong constraints on the temporal evolution of the bulk viscosity coefficient, temperature and relaxation time, thus leading to the possibility of obtaining the bulk v…
In this paper we study the evolution of a LRS Bianchi I Universe, filled with a bulk viscous cosmological fluid in the presence of time varying constants "but" taking into account the effects of a c-variable into the curvature tensor. We find that the only physical models are those which ``constants'' $G$ and $c$ are growing functions on time $t$, while the cosmological constant $Λ$ is a negative decreasing function. In such solutions the energy density obeys the ultrastiff matter equation of state i.e. $ω=1$.
We study the evolution of a flat Friedmann-Robertson- Walker Universe, filled with a bulk viscous cosmological fluid, in the presence of variable gravitational and cosmological constants. The dimensional analysis of the model suggest a proportionality between the bulk viscous pressure of the dissipative fluid and the energy density. With the use of this assumption and with the choice of the standard equations of state for the bulk viscosity coefficient, temperature and relaxation time, the general solution of the field equations can be obtained, with all physical parameters having a power-law …
We study the evolution of a flat Friedmann-Robertson-Walker Universe, filled with a bulk viscous cosmological fluid, in the presence of time varying ``constants''. The dimensional analysis of the model suggests a proportionality between the bulk viscous pressure of the dissipative fluid and the energy density. On using this assumption and with the choice of the standard equations of state for the bulk viscosity coefficient, temperature and relaxation time, the general solution of the field equations can be obtained, with all physical parameters having a power-law time dependence. The symmetry …
We consider the evolution of a flat Friedmann-Robertson-Walker Universe, filled with a causal bulk viscous cosmological fluid, in the presence of variable gravitational and cosmological constants. The basic equation for the Hubble parameter, generalizing the evolution equation in the case of constant gravitational coupling and cosmological term, is derived, under the supplementary assumption that the total energy of the Universe is conserved. By assuming that the cosmological constant is proportional to the square of the Hubble parameter and a power law dependence of the bulk viscosity coeffic…
We analyze the dynamics of a Bianchi I cosmology in the presence of a viscous fluid, causally regularized according to the Lichnerowicz approach. We show how the effect induced by shear viscosity is still able to produce a matter creation phenomenon, meaning that also in the regularized theory we address, the Universe is emerging from a singularity with a vanishing energy density value. We discuss the structure of the singularity in the isotropic limit, when bulk viscosity is the only retained contribution. We see that, as far as viscosity is not a dominant effect, the dynamics of the isotropi…
In this paper, we have investigated the non-adiabatic spherical gravitational collapse in the framework of the $f(R,T)$ theory of gravity with a locally anisotropic fluid that undergoes dissipation in the form of heat flux, free-streaming radiation, and shearing viscosity. The dynamical equations are analyzed in detail, both in the Newtonian and post-Newtonian regimes. Finally we couple the dynamical equations to the full causal transport equation in the context of Israel-Stewart theory of dissipative systems. This yields us a better understanding of the collapse dynamics and may be connected …
Evolution of the bulk viscous matter dominated universe has been analysed using the full causal, Israel-Stewart theory for the evolution of bulk viscous pressure in the context of recent acceleration of the universe. The form of bulk viscosity is taken as $ξ=αρ^{1/2}. $ We obtained analytical solutions for the Hubble parameter and scale factor of the universe. The model parameters have been computed using the Type Ia supernovae observational data. The evolution of the prominent cosmological parameters were obtained. The age of the universe for the best estimated model parameters is found to be…
The behaviour of solutions to the Einstein equations with a causal viscous fluid source is investigated. In this model we consider a spatially flat Robertson-Walker metric, the bulk viscosity coefficient is related to the energy density as $ζ= αρ^{m}$, and the relaxation time is given by $ζ/ρ$. In the case $m = 1/2$ we find the exact solutions and we verify whether they satisfy the energy conditions. Besides, we study analytically the asymptotic stability of several families of solutions for arbitrary $m$. We find that the qualitative asymptotic behaviour in the far future is not altered by re…
In this paper we investigate some properties, including causality, of a particular class of relativistic dissipative fluid theories of divergence type. This set is defined as those theories coming from a statistical description of matter, in the sense that the three tensor fields appearing in the theory can be expressed as the three first momenta of a suitable distribution function. In this set of theories the causality condition for the resulting system of hyperbolic partial differential equations is very simple and allow to identify a subclass of manifestly causal theories, which are so for …
An analysis of the gravitational instability in presence of dissipative effects is addressed. In particular, the standard Jeans Mechanism and the generalization in treating the Universe expansion are both analyzed when bulk viscosity affects the first-order Newtonian dynamics. As results, the perturbation evolution is founded to be damped by dissipative processes and the top-down mechanism of structure fragmentation is suppressed. In such a scheme, the value of the Jeans Mass remains unchanged also in presence of viscosity.
This paper reports a study on the truncated Israel-Stewart formalism for bulk viscosity using the extended holographic Ricci dark energy (EHRDE), where the density of dark energy is given as a combination of the Hubble parameter and its derivative. The equations of motion are integrated and the resulting model is analysed under many aspects, including the state finder parameters and the generalised thermodynamics second law. Under the consideration that the universe is dominated by EHRDE the evolution equation for the bulk viscous pressure $Π$ in the framework of the truncated Israel-Stewart t…
We consider dissipation of surface waves on fluids, with a view to its effects on analogue gravity experiments. We begin by reviewing some general properties of wave dissipation, before restricting our attention to surface waves and the dissipative role played by viscosity there. Finally, with particular focus on water, we consider several experimental setups inspired by analogue gravity: the analogue Hawking effect, the black hole laser, the analogue wormhole, and double bouncing at the wormhole entrance. Dissipative effects are considered in each, and we give estimates for their optimized ex…
We consider cosmological scenarios originating from a single imperfect fluid with bulk viscosity and apply Eckart's and both the full and the truncated Müller-Israel-Stewart's theories as descriptions of the non-equilibrium processes. Our principal objective is to investigate if the dynamical properties of Dark Matter and Dark Energy can be described by a single viscous fluid and how such description changes when a causal theory (Müller-Israel-Stewart's, both in its full and truncated forms) is taken into account instead of Eckart's non-causal theory. To this purpose, we find numerical solutio…
The general solution of the gravitational field equations in the flat Friedmann-Robertson-Walker geometry is obtained in the framework of the full Israel-Stewart-Hiscock theory for a bulk viscous stiff cosmological fluid, with bulk viscosity coefficient proportional to the energy density.
An isotropic and homogeneous cosmological model with a source of dark energy is studied. That source is simulated with a viscous relativistic fluid with minimal causal correction. In this model the restrictions on the parameters coming from the following conditions are analized: a) energy density without singularities along time, b) scale factor increasing with time, c) universe accelerated at present time, d) state equation for dark energy with "w" bounded and close to -1. It is found that those conditions are satified for the following two cases. i) When the transport coefficient (τ_{Π}), as…
This paper presents a hydrodynamic and thermodynamic treatment of a radiant star model that undergoes a dissipative gravitational collapse, from a certain initial configuration until it becomes a black hole. The collapsing star consists of a locally anisotropic non-perfect fluid, where we explore the consequences of including viscous pressures, both shear and bulk viscosities, as well as radial heat flow. We analyze the temporal evolution of the heat flux, mass function, luminosity perceived by an observer at infinity and the effective surface temperature. It is shown that this simple exact mo…
Effective theory arguments are used to derive the most general energy-momentum tensor of a relativistic viscous fluid with an arbitrary equation of state (in the absence of other conserved currents) that is first-order in the derivatives of the energy density and flow velocity and does not include extended variables such as in Mueller-Israel-Stewart-like theories. This energy-momentum tensor leads to a causal theory, provided one abandons the usual conventions for the out-of-equilibrium hydrodynamic variables put forward by Landau-Lifshitz and Eckart. In particular, causality requires nonzero …
We consider the dynamics of a viscous cosmological fluid in the generalized Randall-Sundrum model for an anisotropic, Bianchi type I brane. To describe the dissipative effects we use the Israel-Hiscock-Stewart full causal thermodynamic theory. By assuming that the matter on the brane obeys a linear barotropic equation of state, and the bulk viscous pressure has a power law dependence on the energy density, the general solution of the field equations can be obtained in an exact parametric form. The obtained solutions describe generally a non-inflationary brane world. In the large time limit the…
In this talk, we discuss one of the dissipative processes which likely take place in the Early Universe. We assume that the matter filling the isotropic and homogeneous background is to be described by a relativistic viscous fluid characterized by an ultra-relativistic equation of state and finite bulk viscosity deduced from recent lattice QCD calculations and heavy-ion collisions experiments. We concentrate our treatment to bulk viscosity as one of the essential dissipative processes in the rapidly expanding Early Universe and deduce the dependence of the scale factor and Hubble parameter on …
We study a closed model of the universe filled with viscous fluid and quintessence matter components in a Brans-Dicke type cosmological model. The dynamical equations imply that the universe may look like an accelerated flat Friedmann-Robertson-Walker universe at low redshift. We consider here dissipative processes which follow a causal thermodynamics. The theory is applied to viscous fluid inflation, where accepted values for the total entropy in the observable universe is obtained.
The truncated Israel-Stewart theory of irreversible thermodynamics is used to describe the bulk viscous pressure and the anisotropic stress in a class of spatially homogeneous viscous fluid cosmological models. The governing system of differential equations is written in terms of dimensionless variables and a set of dimensionless equations of state is utilized to complete the system. The resulting dynamical system is then analyzed using standard geometric techniques. It is found that the presence of anisotropic stress plays a dominant role in the evolution of the anisotropic models. In particu…
The present works deals with gravitational collapse of cylindrical viscous heat conducting anisotropic fluid following the work of Misner and Sharp. Using Darmois matching conditions, the dynamical equations are derived and the effect of charge and dissipative quantities over the cylindrical collapse are analyzed. Finally, using the Miller-Israel-Steward causal thermodynamic theory, the transport equation for heat flux are derived and its influence on collapsing system has been studied.
The Full (non--truncated) Israel--Stewart theory of bulk viscosity is applied to dissipative FRW spacetimes. Dimensionless variables and dimensionless equations of state are used to write the Einstein--thermodynamic equations as a plane autonomous system and the qualitative behaviour of this system is determined. Entropy production in these models is also discussed.
We present the first numerical analysis of causal, stable first-order relativistic hydrodynamics with ideal gas microphysics, based in the formalism developed by Bemfica, Disconzi, Noronha, and Kovtun (BDNK theory). The BDNK approach provides definitions for the conserved stress-energy tensor and baryon current, and rigorously proves causality, local well-posedness, strong hyperbolicity, and linear stability (about equilibrium) for the equations of motion, subject to a set of coupled nonlinear inequalities involving the undetermined model coefficients (the choice for which defines the "hydrody…
A new approach is described to help improve the foundations of relativistic viscous fluid dynamics and its coupling to general relativity. Focusing on neutral conformal fluids constructed solely in terms of hydrodynamic variables, we derive the most general viscous energy-momentum tensor yielding equations of motion of second order in the derivatives, which is shown to provide a novel type of generalization of the relativistic Navier-Stokes equations for which causality holds. We show how this energy-momentum tensor may be derived from conformal kinetic theory. We rigorously prove existence, u…
We investigate the role of bulk viscous pressure on the warm inflationary modified Chaplygin gas in brane-world framework in the presence of standard scalar field. We assume the intermediate inflationary scenario in strong dissipative regime and constructed the inflaton, potential, entropy density, slow-roll parameters, scalar and tensor power spectra, scalar spectral index and tensor-to-scalar ratio. We develop various trajectories such as $n_s - N$, $n_s - r$ and $n_s - α_s$ (where $n_s$ is the spectral index, $α_s$ is the running of spectral index, $N$ is the number of e-folds and $r$ is te…
In this paper we study the consistency of a cosmological model representing a universe filled with a one-component dissipative dark matter fluid, in the framework of the causal Israel-Stewart theory, where a general expression arising from perturbation analysis for the relaxation time $τ$ is used. This model is described by an exact analytic solution recently found in [N. Cruz, E. González and G. Palma, Gen. Rel. Grav. \textbf{52}, 62 (2020), which depends on several model parameters as well as integration constants, allowing the use of Type Ia Supernovae and Observational Hubble data to perfo…
The effects of bulk viscosity are examined for inflationary dynamics in which dissipation and thermalization are present. A complete stability analysis is done for the background inflaton evolution equations, which includes both inflaton dissipation and radiation bulk viscous effects. Three representative approaches of bulk viscous irreversible thermodynamics are analyzed: the Eckart noncausal theory, the linear and causal theory of Israel-Stewart and a more recent nonlinear and causal bulk viscous theory. It is found that the causal theories allow for larger bulk viscosities before encounteri…
In this work, we present a study of a purely kinetic k-essence model, characterized basically by a parameter $α$ in presence of a bulk dissipative term, whose relationship between viscous pressure $Π$ and energy density $ρ$ of the background follows a polytropic type law $Π\propto ρ^{λ+1/2}$, where $λ$, in principle, is a parameter without restrictions. Analytical solutions for the energy density of the k-essence field are found in two specific cases: $λ=1/2$ and $λ=(1-α)/2α$, and then we show that these solutions posses the same functional form than the non-viscous counterpart. Finally, both …
We analyze the dynamics of models of warm inflation with general dissipative effects. We consider phenomenological terms both for the inflaton decay rate and for viscous effects within matter. We provide a classification of the asymptotic behavior of these models and show that the existence of a late-time scaling regime depends not only on an asymptotic behavior of the scalar field potential, but also on an appropriate asymptotic behavior of the inflaton decay rate. There are scaling solutions whenever the latter evolves to become proportional to the Hubble rate of expansion regardless of the …
In this work we present an analysis of the phantom zone in a causal viscous cosmology from a thermodynamic point of view. In this description we consider a chemical potential and the approach of irreversible processes. We assume a flat universe filled with a single dissipative fluid described by a barotropic equation of state, $p = ωρ$. This model allows to construct a negative chemical potential for the phantom regime but also this construction allows us to have positive definite temperature and entropy.
The dynamical system behaviour and thermal evolution of a homogeneous and isotropic dissipative universe are analyzed. The dissipation is driven by the bulk viscosity $ξ= αρ^s $ and the evolution of bulk viscous pressure is described using the full causal Israel-Stewart theory. We find that for $s=1/2$ the model possesses a prior decelerated epoch which is unstable and a stable future accelerated epoch. From the thermodynamic analysis, we have verified that the local as well as the generalised second law of thermodynamics are satisfied throughout the evolution of the universe. We also show tha…
We present a unified causal general relativistic formulation of dissipative and non-dissipative continuum mechanics. The presented theory is the first general relativistic theory that can deal simultaneously with viscous fluids as well as irreversible deformations in solids and hence it also provides a fully covariant formulation of the Newtonian continuum mechanics in arbitrary curvilinear spacetimes. In such a formulation, the matter is considered as a Riemann-Cartan manifold with non-vanishing torsion and the main field of the theory being the non-holonomic basis tetrad field also called fo…
In this work we explore a new cosmological solution for an universe filled with one dissipative fluid, described by a barotropic EoS $p = ωρ$, in the framework of the full Israel-Stewart theory. The form of the bulk viscosity has been assumed of the form $ξ= ξ_{0}ρ^{1/2}$. 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 $ω$, $ξ_{0}$, $c_{b}$ accelerated and decelerated c…
