We have constructed a spherically symmetric structure model in a cosmological background filled with perfect fluid with non-vanishing pressure as an exact solution of Einstein equations using the Lemaître solution. To study its local and quasi-local characteristics including the novel features of its central black hole, we have suggested an algorithm to integrate the equations numerically. The result shows intriguing effects of the pressure inside the structure. The evolution of the central black hole within the FRW universe, its decoupling from the expanding parts of the model, the structure of its space-like apparent horizon, the limiting case of the dynamical horizon tending to a slowly evolving horizon, and the decreasing mass in-fall to the black hole is also studied. The cosmological redshift of a light emitted from the cosmological structure to an observer in the FRW background is also calculated. This cosmological redshift includes local and cosmic part which are explicitly separated. We have also formulated a modified NFW density profile for a structure to match the exact solution conditions.
Different characteristic of matter influencing the evolution of the Universe has been simulated by means of a nonlinear spinor field. Exploiting the spinor description of perfect fluid and dark energy evolution of the Universe given by an anisotropic Bianchi type-I (BI) or isotropic Friedmann-Robertson-Walker (FRW) one has been studied.
We impose perfect fluid concept along with slow expansion approximation to derive new solutions which, considering non-static spherically symmetric metrics, can be treated as Black Holes (BHs). We will refer to these solutions as Quasi BHs. Mathematical and physical features such as Killing vectors, singularities, and mass have been studied. Their horizons and thermodynamic properties have also been investigated. In addition, relationship with other related works (including McVittie's) are described.
We systematically study the evolution of the Friedmann-Robertson-Walker (FRW) universe coupled with a cosmological constant $Λ$ and a perfect fluid that has the equation of state $p=wρ$, where $p$ and $ρ$ denote, respectively, the pressure and energy density of the fluid, and $w$ is an arbitrary real constant. Depending on the specific values of $w,\; Λ$, and the curvature $k$ of 3-dimensional space, we separate all of the solutions into various cases. In each case the main properties of the evolution are given in detail, including the periods of deceleration and/or acceleration, and the exist…
We employ recently developed approximation methods in the hybrid quantization of the Gowdy $T^3$ model with linear polarization and a massless scalar field to obtain physically interesting solutions of this inhomogeneous cosmology. More specifically, we propose approximate solutions of the quantum Gowdy model constructed in such a way that, for the Hamiltonian constraint, they effectively behave as those corresponding to a flat homogeneous and isotropic universe filled with a perfect fluid, even though these quantum states are far from being homogeneous and isotropic. We analyze how one can ge…
We consider the cosmological model which allows to describe on equal footing the evolution of matter in the universe on the time interval from the inflation till the domination of dark energy. The matter is considered as a two-component perfect fluid imitated by homogeneous scalar fields between which there is energy exchange. Dark energy is represented by the cosmological constant, which is supposed invariable during the whole evolution of the universe. The matter changes its equation of state with time, so that the era of radiation domination in the early universe smoothly passes into the er…
We make a first principle study of gravitational pressure in cosmic thermodynamics. The pressure is directly derived from the unified first law, in fact the Einstein field equation in spherically symmetric spacetime. By using this pressure, we obtain the thermodynamics for the FRW universe, especially presenting the gravitational equation of state for the FRW spacetime itself, i.e. $P=P(R_A, T)$ for the first time. Furthermore, we study the Joule-Thomson expansion as an application of the thermodynamic equation of state to find the cooling-heating property of the FRW universe. We demonstrate t…
We discuss a model for a universe with discrete matter content instead of the continuous perfect fluid taken in FRW models. We show how the redshift in such a universe deviates from the corresponding one in an FRW cosmology. This illustrates the fact that averaging the matter content in a universe and then evolving it in time, is not the same as evolving a universe with discrete matter content. The main reason for such deviation is the fact that the photons in such a universe mainly travel in an empty space rather than the continuous perfect fluid in FRW geometry.
In the paper, the temperature associated with a dynamical spherically symmetric black hole or with a cosmological horizon is investigated from the point of view of a point-like detector. First, we briefly review the Hamilton-Jacobi tunneling method for a generic dynamical spherically symmetric space-time, and present two applications of the tunneling method. Then, we apply a well-known relativistic quantum theoretical technique, namely the Unruh-DeWitt detector formalism for a conformally coupled scalar field in a generic FRW space-time. As an application, for the generic static black hole cas…
In this article we investigate and develop specific aspects of Friedmann-Robertson-Walker (FRW) scalar field cosmologies related to the interpretation that canonical and phantom scalar field sources may be interpreted as cosmological configurations with a mixture of two interacting barotropic perfect fluids: a matter component $ρ_1(t)$ with a stiff equation of state ($p_1=ρ_1$), and an "effective vacuum energy" $ρ_2(t)$ with a cosmological constant equation of state ($p_2=-ρ_2$). An important characteristic of this alternative equivalent formulation in the framework of interacting cosmologies …
Collapsing process is studied in special type of inhomogeneous spherically symmetric space-time model (known as IFRW model), having no time-like Killing vector field. The matter field for collapse dynamics is considered to be perfect fluid with anisotropic pressure. The main issue of the present investigation is to examine whether the end state of the collapse to be a naked singularity or a black hole. Finally, null geodesics is studied near the singularity.
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.
We study the tachyon scalar field model in flat FRW cosmology with the particular potential $ϕ^{-2}$ and the scale factor behavior $a(t)=t^n$. We consider the spherical collapse model and investigate the effects of the tachyon scalar field on the structure formation in flat FRW universe. We calculate $δ_{c}(z_{c})$, $λ(z_{c})$, $ξ(z_{c})$, $Δ_{V}(z_{c})$, $\log [νf(ν)]$ and $\log [n(k)]$ for the tachyon scalar field model and compare the results with the results of EdS model and $ΛCDM$ model. It is shown that in the tachyon scalar field model the structure formation may occur earlier, in compa…
We study FRW homogeneous cosmological solutions in the recently found ghost free massive gravity. In previous works it was shown that when the additional extra metric, needed to generate the mass term, is taken as non-dynamical and flat, no homogeneous FRW cosmology exists. We show that, when the additional metric is a dynamical field, a perfectly safe FRW universe exists. FRW solutions fall in two branches. In the first branch the massive deformation is equivalent to an effectively generated cosmological constant whose scale is determined by the graviton mass. The second branch is quite rich:…
In this work, we present a phase space analysis of a spatially flat Friedmann $-$Robertson$-$Walker (FRW) model in which the dark matter fluid is modeled as an imperfect fluid having bulk viscosity. The bulk viscosity is governed by the Maxwell$-$Cattaneo approach. The rest of the components of the model: radiation and dark energy are treated as perfect fluids. Imposing a complete cosmological dynamics and taking into account a recent constraint on the dark matter equation of state (EOS), we obtain bound on the bulk viscosity. The results point towards the possibility of describing not only th…
In this paper, we investigate the thermodynamics especially the Hawking-Page-like phase transition of the McVittie space-time. We formulate the first law of thermodynamics for the McVittie black hole, and find that the work density $W$ of the perfect fluid plays the role of the thermodynamic pressure, i.e. $P$:=$-W$. We also construct the thermodynamic equation of state for the McVittie black hole. Most importantly, by analysing the Gibbs free energy, we find that the Hawking-Page-like phase transition from FRW spacetime to McVittie black hole is possible in the case $P>0$.
For the description of the early inflation, and acceleration expansion of the Universe, compatible with observational data, the 5D noncompact Kaluza--Klein cosmology is investigated. It is proposed that the 5D space is filled with a null perfect fluid, resulting a perfect fluid in 4D universe, plus one along the fifth dimension. By analyzing the reduced field equations for flat FRW model, we show the early inflationary behavior and current acceleration of the universe.
We analyze the global nonlinear stability of FRW (Friedmann-Robertson-Walker) spacetimes in presence of an irrotational perfect fluid. We assume that the fluid is governed by the so-called (generalized) Chaplygin equation of state relating the pressure to the mass-energy density. We express the Einstein equations in wave gauge as a systems of coupled nonlinear wave equations and by performing a suitable conformal transformation, we are able to analyze the global behavior of solutions in future timelike directions. We establish that the (3+1)-spacetime metric and the mass density and velocity v…
In an open Friedmann-Robertson-Walker (FRW) space background, we study the classical and quantum cosmological models in the framework of the recently proposed nonlinear massive gravity theory. Although the constraints which are present in this theory prevent it from admitting the flat and closed FRW models as its cosmological solutions, for the open FRW universe, it is not the case. We have shown that, either in the absence of matter or in the presence of a perfect fluid, the classical field equations of such a theory adopt physical solutions for the open FRW model, in which the mass term show…
In this paper we find new solutions for the so called Einstein-Chern-Simons Friedmann-Robertson-Walker field equations studied in refs. (Phys. Rev. D 84 (2011) 063506, Eur. Phys. J. C 74 (2014) 3087). We consider three cases:(i) in the first case we find some solutions of the five-dimensional ChS-FRW field equations when the $h^a$ field is a perfect fluid that obeys a barotropic equation of state; (ii) in the second case we study the solutions, for the cases $γ=1/2,\ 3/4$, when the $h^a$ field is a five dimensional politropic fluid that obeys the equation $P^{(h)}=ω^{(h)}ρ^{(h)γ}$; (iii) in th…
We show that Einstein's field equations for spatially flat Friedmann-Robertson-Walker (FRW) space times have a form invariance symmetry (FIS) realized by the form invariance transformations (FIT) which are indeed generated by an invertible function of the source energy density. These transformations act on the Hubble expansion rate, the energy density, and pressure of the cosmic fluid; likewise such transformations are endowed with a Lie group structure. Each representation of this group is associated with a particular fluid and consequently a determined cosmology, so that, the FIS defines a s…
In the context of the Teleparallel Equivalent of General Relativity (TEGR) one can obtain an alternative insight into General Relativity, as has been shown in addressing properties as energy, momentum and angular momentum of the gravitational field. In this paper, we apply the definition, that arises from the field equation of the the TEGR, for the stress-energy-momentum tensor of the gravitational field, whose spatial components naturally lead to the definition of gravitational pressure, to compute the total space-time pressure, due to the gravitational and matter fields, over a spherical, sp…
We present the exact equations governing the dynamics of a spherically-symmetric inhomogeneous model with n decoupled and non-comoving perfect fluids. Thanks to the use of physically meaningful quantities we write the set of 3+2n equations in a concise and transparent way. The n perfect fluids can have general equations of state, thus making the model extremely flexible to study a large variety of cosmological and astrophysical problems. As applications we consider a model sourced by two non-comoving dust components and a cosmological constant, and a model featuring dust and a dark energy comp…
We study Friedmann-Robertson-Walker cosmological models with matter content composed of two perfect fluids $ρ_1$ and $ρ_2$, with barotropic pressure densities $p_1/ ρ_1=ω_1=const$ and $p_2/ ρ_2=ω_2=const$, where one of the energy densities is given by $ρ_1=C_1 a^α+ C_2 a^β$, with $C_1$, $C_2$, $α$ and $β$ taking constant values. We solve the field equations by using the conservation equation without breaking it into two interacting parts with the help of a coupling interacting term $Q$. Nevertheless, with the found solution may be associated an interacting term $Q$, and then a number of cosmol…
In this work we investigate the spherical collapse model in flat FRW universe containing dark energy component. We consider the Holographic Dark Energy (HDE) model as a dynamical dark energy scenario with slowly time varying EoS parameter $w_Λ$ in order to calculate the effect of dark energy on the scenario of structure formation in the universe. We first calculate the evolution of density perturbation in linear regime for both phantom and quintessence behavior of HDE model and compare the results with standard CDM and $Λ$ CDM models. Then we calculate the evolution of two parameters character…
The present work investigates the gravitational collapse of a perfect fluid in $f(R)$ gravity models. For a general $f(R)$ theory, it is shown analytically that a collapse is quite possible. The singularity formed as a result of the collapse is found to be a curvature singularity of shell focusing type. The possibility of the formation of an apparent horizon hiding the central singularity depends on the initial conditions.
We study spherically-symmetric solutions in Massive Gravity generated by matter sources with polytropic equation of state. We concentrate in the non-perturbative regime where the mass term non-linearities are important, and present the main features of the solutions.
We investigate spherically symmetric perfect-fluid spacetimes and discuss the existence and stability of a dividing shell separating expanding and collapsing regions. We perform a 3+1 splitting and obtain gauge invariant conditions relating the intrinsic spatial curvature of the shells to the Misner-Sharp mass and to a function of the pressure that we introduce and that generalizes the Tolman-Oppenheimer-Volkoff equilibrium condition. We find that surfaces fulfilling those two conditions fit, locally, the requirements of a dividing shell and we argue that cosmological initial conditions should…
The general analytical solution for the static spherically symmetric metric supported by a perfect fluid with isothermal (proportional) equation-of-state $p = w ρ$ is not known at the time of this writing, except for the trivial cases $w=0$ and $w=-1$; and for $w=-1/3$. We show that if Buchdahl coordinates are used, the problem becomes analytically solvable for $w=-1/5$; display and discuss the solution(s), and exhibit the connection of this case to the $w=-1$ case.
