A static, spherically symmetric spacetime with negative pressures is conjectured inside a star. The gravitational field is repulsive and so a central singularity is avoided. The positive energy density and the pressures of the imperfect fluid are finite everywhere. The Tolman-Komar energy of the space is negative, as for a de Sitter geometry. From the Darmois-Israel junction conditions on the star surface one finds the constant length $b$ from the metric and the expression of the surface tension $σ$ of the thin shell separating the interior from the Schwarzschild exterior. Some properties of the timelike and null geodesics in the Painleve-Gullstrand coordinates are investigated.
Self-consistent solutions to interacting spinor and scalar field equations in General Relativity are studied for the case of Bianchi type-I space-time filled with perfect fluid. The initial and the asymptotic behavior of the field functions and the metric one has been thoroughly studied.
Rotating and twisting locally rotationally symmetric imperfect fluids in general relativity admit a much larger set of solutions than the self-similar ones recently suggested in the literature. Explicit forms of the metrics are given and the self-similar sub-cases are discussed.
We construct a cosmological toy model based on a Finslerian structure of space-time. In particular, we are interested in a specific Finslerian Lorentz violating theory based on a curved version of Cohen and Glashow's Very Special Relativity. The osculation of a Finslerian manifold to a Riemannian leads to the limit of Relativistic Cosmology, for a specified observer. A modified flat FRW cosmology is produced. The analogue of a zero energy particle unfolds some special properties of the dynamics. The kinematical equations of motion are affected by local anisotropies. Seeds of Lorentz Violations…
The Brans-Dicke-like field of scalar-tensor gravity can be described as an imperfect fluid in an approach in which the field equations are regarded as effective Einstein equations. After completing this approach we recover, as a special case, the known effective fluid for a scalar coupled nonminimally to the Ricci curvature and we describe the imperfect fluid equivalent of f(R) gravity. A symmetry of electrovacuum Brans-Dicke gravity is translated into a symmetry of the corresponding effective fluid. The discussion is valid for any spacetime geometry.
We consider a self-consistent system of spinor and scalar fields within the framework of a Bianchi type I gravitational field filled with viscous fluid in presence of a $Λ$ term. Exact self-consistent solutions to the corresponding spinor, scalar and BI gravitational field equations are obtained in terms of $τ$, where $τ$ is the volume scale of BI universe. System of equations for $τ$ and $\ve$, where $\ve$ is the energy of the viscous fluid, is deduced. Some special cases allowing exact solutions are thoroughly studied.
When solving the equations of General Relativity in a symmetric sector, it is natural to consider the same symmetry for the geometry and stress-energy. This implies that for static and isotropic spacetimes, the most general natural stress-energy tensor is a sum of a perfect fluid and a radial imperfect fluid component. In the special situations where the perfect fluid component vanishes or is a spacetime constant, the solutions to Einstein's equations can be thought of as modified Schwarzschild and Schwarzschild-de Sitter spaces. Exact solutions of this type are derived and it is shown that wh…
We study the thermodynamics of the universe containing perfect fluid with equation of state $p=ωρ,ω$ is variable. Here we choose $ω$ to be a function of the red shift variable $z$ and four different choices of $ω$ has been investigated. Also the laws of thermodynamics are examined considering the universe bounded by the horizon (apparent) as a thermodynamical system.
Self-consistent solutions to nonlinear spinor field equations in General Relativity have been studied for the case of Bianchi type-I space-time filled with perfect fluid. The initial and the asymptotic behavior of the field functions and the metric one has been thoroughly studied. It should be emphasized the absence of initial singularity for some types of solutions and also the isotropic mode of space-time expansion in some special cases.
So far all known singularity-free cosmological models are cylindrically symmetric. Here we present a new family of spherically symmetric non-singular models filled with imperfect fluid and radial heat flow, and satisfying the weak and strong energy conditions. For large $t$ anisotropy in pressure and heat flux tend to vanish leading to a perfect fluid. There is a free function of time in the model, which can be suitably chosen for non-singular behaviour and there exist multiplicity of such choices.
We revisit the issue of the fluid description of minimally coupled scalar fields. While in a cosmological setup the interpretation of a time-evolving scalar field as a perfect fluid is well-understood, the situation is more intricate when the scalar field is static, but has a spatial gradient, a situation motivated by black hole perturbations in scalar-tensor theories. Then the scalar field is interpreted as either a particular imperfect fluid of type I or a superposition of a pair of leftgoing (incoming) and rightgoing (outgoing) null dusts with a perfect fluid. Finally, when the scalar gradi…
We present a new prescription for analysing cosmological perturbations in a more-general class of scalar-field dark-energy models where the energy-momentum tensor has an imperfect-fluid form. This class includes Brans-Dicke models, f(R) gravity, theories with kinetic gravity braiding and generalised galileons. We employ the intuitive language of fluids, allowing us to explicitly maintain a dependence on physical and potentially measurable properties. We demonstrate that hydrodynamics is not always a valid description for describing cosmological perturbations in general scalar-field theories an…
We study five dimensional cosmological models with four dimensional hypersufaces of the Bianchi type I and V. In this way the five dimensional vacuum field equations $\rm G_{AB} = 0$, led us to four dimensional matter equations $\rm G_{μν}=T_{μν}$ and the matter is interpreted as a purely geometrical property of a fifth dimension. Also, we find that the energy-momentum tensor induced from the fifth dimension has the structure of an imperfect fluid that has dissipative terms.
Self-consistent system of spinor, scalar and BI gravitational fields in presence of magneto-fluid and $Λ$-term is considered. Assuming that the expansion of the BI universe is proportional to the $σ_1^1$ component of the shear tensor, exact solutions for the metric functions, as well as for scalar and spinor fields are obtained. For a non-positive $Λ$ the initially anisotropic space-time becomes isotropic one in the process of expansion, whereas, for $Λ> 0$ an oscillatory mode of expansion of the BI model occurs.
We derive a shortcut stationary metric formula for generating imperfect fluid rotating solutions, in Boyer-Lindquist coordinates, from spherically symmetric static ones. We explore the properties of the curvature scalar and stress-energy tensor for all types of rotating regular solutions we can generate without restricting ourselves to specific examples of regular solutions (regular black holes or wormholes). We show through examples how it is generally possible to generate an imperfect fluid regular rotating solution via radial coordinate transformations. We derive rotating wormholes that are…
An inhomogeneous fluid in accelerated motion is investigated. When the velocity field $v(x)$ is not constant, the geometry viewed by a static observer is curved, as if the observer were immersed in a gravitational field. A velocity-dependent semiclassical gravitational potential is introduced, which obeys an Yukawa-type equation, written in Cartesian coordinates. The timelike and null geodesic equations are investigated. One finds that the fluid has zero energy density corresponding to the perfect fluid part but nonzero anisotropic energy density. The pressures will no longer depend on $\hbar$…
We consider a system of nonlinear spinor and a Bianchi type I gravitational fields in presence of viscous fluid. The nonlinear term in the spinor field Lagrangian is chosen to be $λF$, with $λ$ being a self-coupling constant and $F$ being a function of the invariants $I$ an $J$ constructed from bilinear spinor forms $S$ and $P$. Self-consistent solutions to the spinor and BI gravitational field equations are obtained in terms of $τ$, where $τ$ is the volume scale of BI universe. System of equations for $τ$ and $\ve$, where $\ve$ is the energy of the viscous fluid, is deduced. This system is so…
The first-order general relativistic theory of a generic dissipative (heat-conducting, viscous, particle-creating) fluid is rediscussed from a unified covariant frame-independent point of view. By generalizing some previous works in the literature, we derive a formula for the temperature variation rate, which is valid both in Eckart's (particle) and in the Landau-Lifshitz (energy) frames. Particular attention is paid to the case of gravitational particle creation and its possible cross-effect with the bulk viscosity mechanism.
In this paper we show that an equivalence between Horndeski and beyond Horndeski theories and general relativity with an effective imperfect fluid can be formally established. The formal equivalence is discussed for several particular cases of interest. Working in the cosmological framework, it is shown that, while the effective stress-energy tensor of viable Horndeski theories is formally equivalent to that of an imperfect fluid with anisotropic stresses and vanishing heat flux vector, the effective stress-energy tensor of beyond Horndeski theories is equivalent to the one of a perfect fluid …
We investigate how various inflationary and bouncing cosmologies can be realized by imperfect fluids with a generalized equation of state, in the context of both classical and loop quantum cosmology. With regards to the inflationary cosmologies, we study the intermediate inflation scenario, the $R^2$ inflation scenario and two constant-roll inflation scenarios and with regards to the bouncing cosmologies we study the matter bounce scenario, the singular bounce and the super bounce scenario. Within the context of the classical cosmology, we calculate the spectral index of the power spectrum of …
Extensions of Einstein's General Relativity (GR) can formally be given a GR structure in which additional geometric degrees of freedom are mapped on an effective energy-momentum tensor. The corresponding effective cosmic medium can then be modeled as an imperfect fluid within GR. The imperfect fluid structure allows us to include, on a phenomenological basis, anisotropic stresses and energy fluxes which are considered as potential signatures for deviations from the cosmological standard $Λ$-cold-dark-matter ($Λ$CDM) model. As an example, we consider the dynamics of a scalar-tensor extension of…
We present a standard hydrodynamical description for non-canonical scalar field theories with kinetic gravity braiding. In particular, this picture applies to the simplest galileons and k-essence. The fluid variables not only have a clear physical meaning but also drastically simplify the analysis of the system. The fluid carries charges corresponding to shifts in field space. This shift-charge current contains a spatial part responsible for diffusion of the charges. Moreover, in the incompressible limit, the equation of motion becomes the standard diffusion equation. The fluid is indeed imper…
In this paper, we study the equation of state admissible for a flat FRW models filled with a bulk viscous fluid by using the Lie group method. It is founded that the model admits scaling symmetries iff the bulk viscous parameter $γ=1/2$. In this case, it is found that the main quantities follow a power law solution and in particular the bulk viscous pressure $Π$ has the same order of magnitude as the energy density $ρ,$ in such a way that it is possible to formulate the equation of state $Π=\varkappa ρ,$ where $\varkappa \in \mathbb{R}^{-}$ (i.e. is a negative numerical constant)$.$ If we assu…
A generalized equation of state corresponding to a model that includes a Chaplygin gas and a viscous term is investigated, in the context of the reconstruction program in scalar field cosmology. The corresponding inflationary model parameters can be conveniently adjusted in order to reproduce the most recent PLANCK data. The influence of the Chaplygin gas term contribution, in relation with previous models, is discussed. Exit from inflation is shown to occur quite naturally in the new model.
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…
This paper tries to obtain a simple picture of several aspects of the mode structure in relativistic non-equilibrium thermodynamics. Its pedagogical focus is on the relation between long-wavelength perturbation modes of the causal Müller-Israel-Stewart (MIS) theory and those of the traditional Eckart theory. Principally, this issue was clarified in a series of papers by Hiscock and Lindblom (see [8-10]). Here, I put together some essential features which do not require the entire formalism of the complete theory.
We study the evolution of an anisotropic shear-free fluid with heat flux and kinematic self-similarity of the second kind. We found a class of solution to the Einstein field equations by assuming that the part of the tangential pressure which is explicitly time dependent of the fluid is zero and that the fluid moves along time-like geodesics. The energy conditions, geometrical and physical properties of the solutions are studied. The energy conditions are all satisfied at the beginning of the collapse but when the system approaches the singularity the energy conditions are violated, allowing f…
The tunneling rate, with exact prefactor, is calculated to first order in \hbar for a closed FRW universe filled with perfect fluid violating the strong energy condition. The calculations are performed by applying the dilute-instanton approximation on the corresponding Duru-Kleinert path integral. It is shown that a closed FRW universe filled with a perfect fluid with small violation of strong energy condition is more probable to tunnel than the same universe with large violation of strong energy condition.
We consider Bianchi VI spacetime, which also can be reduced to Bianchi types VI0-V-III-I. We initially consider the most general form of the energy-momentum tensor which yields anisotropic stress and heat flow. We then derive an energy-momentum tensor that couples with the spatial curvature in a way so as to cancel out the terms that arise due to the spatial curvature in the evolution equations of the Einstein field equations. We obtain exact solutions for the universes indefinetly expanding with constant mean deceleration parameter. The solutions are beriefly discussed for each Bianchi type. …
We study integrability by quadrature of a spatially flat Friedmann model containing both a minimally coupled scalar field $ϕ$ with an exponential potential $V(ϕ)\sim\exp[-\sqrt{6}σκϕ]$, $κ=\sqrt{8πG_N}$, of arbitrary sign and a perfect fluid with barotropic equation of state $p=(1-h)ρ$. From the mathematical view point the model is pseudo-Euclidean Toda-like system with 2 degrees of freedom. We apply the methods developed in our previous papers, based on the Minkowsky-like geometry for 2 characteristic vectors depending on the parameters $σ$ and $h$. In general case the problem is reduced to i…
In this article, we considered the bulk viscous fluid in the formalism of modified gravity in which the general form of a gravitational action is $f(R, T)$ function, where $R$ is the curvature scalar and $T$ is the trace of the energy momentum tensor within the frame of flat FRW space time. The cosmological model dominated by bulk viscous matter with total bulk viscous coefficient expressed as a linear combination of the velocity and acceleration of the expansion of the universe in such a way that $ξ=ξ_0+ξ_1\frac{\dot{a}}{a}+ξ_2\frac{\ddot{a}}{\dot{a}}$, where $ξ_0$, $ξ_1$ and $ξ_2$ are consta…
We have considered a model of two component mixture i.e., mixture of Chaplygin gas and barotropic fluid with tachyonic field. In the case, when they have no interaction then both of them retain their own properties. Let us consider an energy flow between barotropic and tachyonic fluids. In both the cases we find the exact solutions for the tachyonic field and the tachyonic potential and show that the tachyonic potential follows the asymptotic behavior. We have considered an interaction between these two fluids by introducing a coupling term. Finally, we have considered a model of three compone…
In this paper, we study damped oscillating form of dark energy for explaining dynamics of universe. First of all, we consider universe is filled with an ideal fluid which has damped oscillating dark energy in terms of this case we calculate several physical quantities such as Hubble parameter, acceleration parameter, energy density, pressure and others for dark energy, dark energy-matter coupling and non-coupling cases. Secondly, we consider as universe is filled with scalar field instead of an ideal fluid we obtain these physical quantities in terms of scalar potential and kinetic term for th…
In this paper we consider spherically symmetric interior spacetimes filled by anisotropic fluids in the context of Hořava gravity and Einstein-aether theory. We assume a specific non-static configuration of the aether vector field and show that the field equations admit a family of exact analytical solutions which can be obtained if one of the two metric coefficients is assigned. We study as an illustrative example the case in which the metric of the interior spacetime reproduces the Newtonian potential of a fluid sphere with constant density.
Coupling dark energy and dark matter through an effective fluid description is a very common procedure in cosmology, however it always remains in comoving coordinates in the special FLRW space. We construct a consistent, general, and covariant formulation, where the interaction is a natural implication of the imperfectness of the fluids. This imperfectness makes difficult the final step towards a robust formulation of interacting fluids, namely the construction of a Lagrangian whose variation would give rise to the interacting equations. Nevertheless, we present a formal solution to this probl…
We consider the Universe at the late stage of its evolution and deep inside the cell of uniformity. At such scales, the Universe is highly inhomogeneous and is filled with inhomogeneities in the form of galaxies and the groups of galaxies. We also suggest that the Universe is filled with a perfect fluid, and its fluctuations have peculiar velocities of the same (non-relativistic) order of magnitude as for the inhomogeneities. In this sense, the inhomogeneities (e.g. galaxies) and fluctuations of perfect fluids are coupled with each other. We clarify some important points of this approach and p…
Wormholes are tunnels connecting different regions in space-time. They were obtained originally as a solution for Einstein's General Relativity theory and according to this theory they need to be filled by an exotic kind of anisotropic matter. In the present sense, by "exotic matter" we mean matter that does not satisfy the energy conditions. In this article we propose the modelling of wormholes within an alternative gravity theory that proposes an extra material (rather than geometrical) term in its gravitational action. Our solutions are obtained from well-known particular cases of the wormh…
It is well known that the canonical quantization of the Friedmann-Lemaître-Robertson-Walker (FLRW) filled with a perfect fluid leads to nonsingular universes which, for later times, behave as their classical counterpart. This means that the expectation value of the scale factor $<a>(t)$ never vanishes and, as $t\to\infty$, we recover the classical expression for the scale factor. In this paper, we show that such universes can be reproduced by classical cosmology given that the universe is filled with an exotic matter. In the case of a perfect fluid, we find an implicit equation of state (EoS).…
We investigate the evolution of the Universe filled with barotropic perfect fluid in Eddington-inspired Born-Infeld gravity. We consider both the isotropic and the anisotropic universe. At the early stage when the energy density is high, the evolution is modified considerably compared with that in general relativity. For the equation-of-state parameter $w>0$, the initial singularity is not accompanied as it was discovered for radiation in earlier work. More interestingly, for pressureless dust ($w=0$), the initial state approaches a de Sitter state. This fact opens a new possibility of singula…
Assuming that the Universe is filled by one single fluid, we present in the context of General Relativity a possible explanation for the acceleration of the Universe. We use ordinary thermodynamics and the fact that small matter perturbations barely propagate in our Universe, to derive a general solution for a single fluid in which the speed of sound vanishes. We find a model that contains $Λ$CDM as a special case, and is compatible with current observational data.
We study a three-component universe filled with dust-like matter in the form of discrete inhomogeneities (e.g., galaxies) and perfect fluids characterized by linear and nonlinear equations of state. Within the cosmic screening approach, we develop the theory of scalar and vector perturbations. None of the energy density contrasts associated with the distinct components is treated as small. Consequently, the derived equations are valid at both sub- and super-horizon scales and enable simulations for a variety of cosmological models.
The aim of this paper is to examine some obtained exact solutions of the Einstein-Maxwell equations, especially their properties from a chronological point of view. Each our spacetime is stationary cylindrically symmetric and it is filled up with an perfect fluid that is electrically charged. There are two classes of solutions and examples of each of them are investigated. We give examples of the first class both for the vanishing as well as for the non-vanishing Lorentz force.
The four-dimensional Friedman flat universe, filled with an ideal fluid with a linear (oscillating) inhomogeneous equation of state (EoS) depending on time, is studied. The equations of motion are solved. It is shown that in some cases there appears a quasi-periodic universe, which repeats the cycles of phantom-type space acceleration. The appearance of future singularities resulting from various choices for the input parameters is discussed.
We investigate a family of inhomogeneous and anisotropic gravitational fields exhibiting a future singularity at a finite value of the proper time. The studied spherically symmetric spacetimes are asymptotically Friedmann-Robertson-Walker at spatial infinity and describe wormhole configurations filled with two matter components: one inhomogeneous and anisotropic fluid and another isotropic and homogeneously distributed fluid, characterized by the supernegative equation of state ω=p/ρ< -1. In previously constructed wormholes, the notion of the phantom energy was used in a more extended sense th…
Cosmology, Gravity, and Astroparticle Physics Group, Center for Theoretical Physics of the Universe, Institute for Basic Science (IBS)（宇宙学、引力与天体物理组，宇宙理论物理中心，基础科学研究院）
The general solution of the field equations in LRS Bianchi-I space-time with perfect fluid equation-of-state (EoS) is presented. The models filled with dust, vacuum energy, Zel'dovich matter and disordered radiation are studied in detail. A unified and systematic treatment of the solutions is presented, and some new solutions are found. The dust, stiff matter and disordered radiation models describe only a decelerated universe, whereas the vacuum energy model exhibits a transition from a decelerated to an accelerated phase.
Combining the equivalence between cosmological particle creation and an effective viscous fluid pressure with the fact that the latter represents a dynamical degree of freedom within the second-order Israel-Stewart theory for imperfect fluids, we reconsider the possibility of accelerated expansion in fluid cosmology. We find an inherent self-limitation for the magnitude of an effective bulk pressure which is due to adiabatic (isentropic) particle production. For a production rate which depends quadratically on the Hubble rate we confirm the existence of solutions which describe a smooth transi…
We study the evolution of the dark energy parameter within the scope of a spatially flat and isotropic Friedmann-Robertson-Walker (FRW) model filled with barotropic fluid and dark energy. To obtain the deterministic solution we choose the scale factor $a(t) = \sqrt{t e^{t}}$ which yields a time dependent deceleration parameter (DP). In doing so we consider the case minimally coupled with dark energy to the perfect fluid as well as direct interaction with it.
The Bianchi type-I universe filled with dark energy from a wet dark fluid has been considered. A new equation of state for the dark energy component of the universe has been used. It is modeled on the equation of state $p=γ(ρ-ρ_\star)$ which can describe a liquid, for example water. The exact solutions to the corresponding field equations are obtained in quadrature form. The solution for constant deceleration parameter have been studied in detail for power-law and exponential forms both. The cases $γ=1$ and $γ=0$ have been also analysed.
We investigate a simple inhomogeneous anisotropic cosmology (plane symmetric $G_2$ model) filled with a tilted perfect fluid undergoing velocity diffusion on a scalar field. Considered are two types of fluid: dust and radiation. We solve the system of Einstein field equations and diffusion equations numerically and demonstrate how the universe evolves towards its future asymptotic state. Also, typical time scales of characteristic processes are determined. The obtained results for dust- and radiation-filled cosmologies are compared to each other and to those in the diffusionless case, giving a…
In this paper, we investigate Bianchi type-$VI$ cosmological model for the universe filled with dark energy and viscous fluid in the presence of cosmological constant. Also, we show accelerating expansion of the universe by drawing volume scale, pressure and energy density versus cosmic time. In order to solve the Einstein field equations, we assume the expansion scalar is proportional to a component of the shear tensor. Therefore, we obtain the directional scale factors and show the EOS parameter crosses over phantom divided-line.
Two new classes of exact interior static solutions of the Einstein equations in homogeneous coordinates for a gravitating ball filled by a Pascal perfect fluid are obtained. Schwarzschild's interior solution of is a special case of these solutions.
The spacetimes for Vaidya's radiating stellar exterior and Kinnersley's photon rocket in a cosmological background are obtained by performing the same conformal transformation as is used to obtain the Robertson-Walker metric from Minkowski spacetime. In the case of the cosmological radiating stellar exterior, a two-fluid solution is found that obeys all of the energy conditions and consists of a null fluid and a perfect fluid that asymptotically falls off to the standard cosmological values for pressure and density at infinite radius. For the cosmological photon rocket, the massless case is fi…
