We investigate the conditions for the (in)stability of the isotropic pressure condition in collapsing spherically symmetric, dissipative fluid distributions. It is found that dissipative fluxes, and/or energy density inhomogeneities and/or the appearance of shear in the fluid flow, force any initially isotropic configuration to abandon such a condition, generating anisotropy in the pressure. To reinforce this conclusion we also present some arguments concerning the axially symmetric case. The consequences ensuing our results are analyzed.
By invoking the relativistic spectral radiance, as derived by Lee and Cleaver [1], the drag radiation pressure of a relativistic planar surface moving through an isotropic radiation field, with which it is in thermal equilibrium, is determined in inertial and non-inertial frames. The forward- and rearward-directed emission radiation pressures are also derived and compared. A fleeting (inertial frames) or ongoing (some non-inertial frames) Carnot cycle is shown to exist as a result of an intra-surfaces temperature gradient. The drag radiation pressure on an object with an arbitrary frontal geom…
In this paper we study static spherically symmetric wormhole solutions sustained by matter sources with isotropic pressure. We show that such spherical wormholes do not exist in the framework of zero-tidal-force wormholes. On the other hand, it is shown that for the often used power-law shape function there is no spherically symmetric traversable wormholes sustained by sources with a linear equation of state $p=ωρ$ for the isotropic pressure, independently of the form of the redshift function $ϕ(r)$. We consider a solution obtained by Tolman at 1939 for describing static spheres of isotropic f…
We found new class of solutions to the Einstein-Maxwell system of equations for charged quark matter within the framework of MIT Bag Model considering a gravitational potential Z(x) proposed by Thirukkanesh and Ragel (2013), which depends on an adjustable parameter n. Variables as the energy density, charge density, pressure and the metric functions are written in terms of elementary and polinominal functions. We show that the form chosen for the gravitational potential allows obtain physically acceptable solutions with any value of the adjustable parameter.
We consider $f(R, T)$ theory of gravity, in which the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar and the trace of the energy-momentum tensor, to study static spherically symmetric wormhole geometries sustained by matter sources with isotropic pressure. According to restrictions on the wormhole geometries, we carefully adopt different strategies to construct solutions with the properties and characteristics of wormholes. Using a completely general procedure, we provide several examples of wormholes in which the matter threading the wormhole throat satisfies a…
Due to R. Beig and W. Simon (1990) there is a uniqueness theorem for static solutions of the Einstein-Euler system which applies to fluid models whose equation of state fulfills certain conditions. In this article it is shown that this uniqueness theorem can be applied to isotropic Vlasov matter, if the gravitational potential well is shallow. To this end we first show how isotropic Vlasov matter can be described as a perfect fluid giving rise to a barotropic equation of state. This 'Vlasov' equation of state is investigated and it is shown analytically that the requirements of the uniqueness …
We study spherically symmetric spacetimes for matter distributions with isotropic pressures. We generate new exact solutions to the Einstein field equations which also contains isotropic pressures. We develop an algorithm that produces a new solution if a particular solution is known. The algorithm leads to a nonlinear Bernoulli equation which can be integrated in terms of arbitrary functions. We use a conformally flat metric to show that the integrals may be expressed in terms of elementary functions. It is important to note that we utilise isotropic coordinates unlike other treatments.
We explore the symmetry group of the pressure isotropy condition in isotropic coordinates finding a rich structure. We work out some specific examples.
We construct a model of a universe filled with a perfect fluid with isotropic particle pressure. The anisotropic plane symmetric Kasner spacetime is used as a seed metric and through a conformal mapping a perfect fluid is generated. The model is inhomogeneous, irrotational, shearing and accelerating. For negative time, the universe is expanding while for positive time it is collapsing. With the aid of graphical three dimensional plots it is established that the density and pressure hypersurfaces are smooth and singularity free. Additionally the sound-speed index is computed and the fluid obeys…
A spatially flat Robertson-Walker spacetime driven by a cosmological constant is non-conformally coupled to a massless scalar field. The equations of semiclassical gravity are explicitly solved for this case, and a self-consistent de Sitter solution associated with the Bunch-Davies vacuum state is found (the effect of the quantum field is to shift slightly the effective cosmological constant). Furthermore, it is shown that the corrected de Sitter spacetime is stable under spatially-isotropic perturbations of the metric and the quantum state. These results are independent of the free renormaliz…
In this paper we study the isotropic cases of static charged fluid spheres in general relativity. For this purpose we consider two different specialization and under these we solve the Einstein-Maxwell field equations in isotropic coordinates. The analytical solutions thus we obtained are matched to the exterior Reissner-Nordström solutions which concern with the values for the metric coefficients $e^ν$ and $e^μ$. We derive the pressure, density, pressure-to-density ratio at the centre of the charged fluid sphere and boundary $R$ of the star. Our conclusion is that static charged fluid spheres…
In present work, we have studied a new stellar distribution model with spherically symmetric matter and an uncharged isotropic distribution in general relativity. In this model, we have considered a particular metric potential. The model is capable to represents some known compact stars like Her X-1,4U 1538-52 and SAX J1808.4-3658.The model satisfy the energy condition and hydrostatic equilibrium equation, i.e., the modified Tolman-Oppenheimer-Volkoff (TOV) equation for uncharged matter. In addition to this, we also present the velocity of sound, surface redshift, and pressure density ratio. T…
The strategy adopted in the original Morris-Thorne wormhole was to retain complete control over the geometry at the expense of certain engineering considerations. The purpose of this paper is to obtain several complete wormhole solutions by assuming a noncommutative-geometry background with a concomitant isotropic-pressure condition. This condition allows us to consider a cosmological setting with a perfect-fluid equation of state. An extended form of the equation generalizes the first solution and subsequently leads to the generalized Chaplygin-gas model and hence to a third solution. The sol…
We present a model for compact stars in the low mass X-ray binaries(LMXBs) and X-ray pulsars using a metric given by John J. Matese and Patrick G. Whitman \citep{Matese and Whitman1980}. Here the field equations are reduced to a system of two algebraic equations considering the isotropic pressure. Compact star candidates 4U 1820-30(radius=10km) in LMXBs, and Her X-1(radius=7.7km), SAX J 1808.4-3658(SS1)(radius=7.07km) and SAX J 1808.4-3658(SS2)(radius=6.35km) in X-ray pulsars satisfy all the energy conditions, TOV-equation and stability condition. From our model, we have derived mass($M$), cen…
In this paper, we derive some new exact solutions of static wormholes in f(T) gravity. We discuss independent cases of the pressure components including isotropic and anisotropic pressure. Lastly we consider radial pressure satisfying a barotropic equation of state. We also check the behavior of null energy condition (NEC) for each case and observe that it is violated for the anisotropic case, while it is satisfied for isotropic and barotropic cases.
The condition for pressure isotropy is reduced to a recurrence equation with variable, rational coefficients of order three. We prove that this difference equation can be solved in general. Consequently we can find an exact solution to the field equations corresponding to a static spherically symmetric gravitational potential in terms of elementary functions. The metric functions, the energy density and the pressure are continuous and well behaved which implies that this solution could be used to model the interior of a relativistic sphere. The model satisfies a barotropic equation of state in…
We study the stability of general relativistic static thick disks, as an application we consider the thick disk generated by applying the ``displace, cut, fill and reflect" method, usually known as the image method, to the Schwarzschild metric in isotropic coordinates. The isotropic Schwarzschild thick disk obtained from this method is the simplest model to describe, in the context of General Relativity, real thick galaxies. The stability under a general first order perturbation of the disk is investigated. The first order perturbation, when applying to the conservation equations, leads to a s…
We study the Einstein-Maxwell system of equations in spherically symmetric gravitational fields for static interior spacetimes. The condition for pressure isotropy is reduced to a recurrence equation with variable, rational coefficients. We demonstrate that this difference equation can be solved in general using mathematical induction. Consequently we can find an explicit exact solution to the Einstein-Maxwell field equations. The metric functions, energy density, pressure and the electric field intensity can be found explicitly. Our result contains models found previously including the neutro…
In the present paper we consider convection and cracking instabilities as well as their interplay. We develop a simple criterion to identify equations of state unstable to convection, and explore the influence of buoyancy on cracking (or overturning) for isotropic and anisotropic relativistic spheres. We show that a density profile $ρ(r)$, monotonous, decreasing and concave , i.e. $ρ' < 0$ and $ρ'' < 0$, will be stable against convection, if the radial sound velocity monotonically decreases outward. We also studied the cracking instability scenarios and found that isotropic models can be unsta…
We discuss the Minkowski stability problem in modified gravity by using dynamical system approach. The method to investigate dynamical stability of Minkowski space was proposed. This method was applied for some modified gravity theories, such as $f(R)$ gravity, $f(R)+αR\Box R$ gravity and scalar-tensor gravity models with non-minimal kinetic coupling. It was shown that in the case of $f(R)$ gravity Minkowski solution asymptotically stable in ghost-free ($f'>0$) and tachyon-free ($f">0$) theories in expanding Universe with respect to isotropic and basic anisotropic perturbations. In the case of…
This manuscript copes with the issue of analyzing the conditions to check the stability of the pressure isotropy condition by taking into account a spherically symmetric dissipative astrophysical configuration with the Palatini $f(R)$ gravity theory. We work out a differential equation in terms of the Weyl scalar that has a crucial part in the analysis of the evolution of the considered system. Using this equation, we devise another stellar equation that characterizes the evolution of anisotropic factor. Later, we assume an axially symmetric configuration and extended our analysis for that par…
We study the behaviour of Bianchi class A universes containing an ultra-stiff isotropic ghost field and a fluid with anisotropic pressures which is also ultra-stiff on the average. This allows us to investigate whether cyclic universe scenarios, like the ekpyrotic model, do indeed lead to isotropisation on approach to a singularity (or bounce) in the presence of dominant ultra-stiff pressure anisotropies. We specialise to consider the closed Bianchi type IX universe and show that when the anisotropic pressures are stiffer on average than any isotropic ultra-stiff fluid then, if they dominate o…
This paper is devoted to study the phase space analysis of isotropic and homogenous universe model by taking a noninteracting mixture of electromagnetic and viscous radiating fluids whose viscous pressure satisfies a nonlinear version of the Israel-Stewart transport equation. We establish an autonomous system of equations by introducing normalized dimensionless variables. In order to analyze stability of the system, we find corresponding critical points for different values of the parameters. We also evaluate power-law scale factor whose behavior indicates different phases of the universe mode…
We show that the inclusion of simple anisotropic pressures stops the isotropic Friedmann universe being a stable attractor as an initial or final singularity is approached when pressures can exceed the energy density. This shows that the situation with isotropic pressures, studied earlier in the context of cyclic and ekpyrotic cosmologies, is not generic, and Kasner-like behaviour occurs when simple pressure anisotropies are present. We find all the asymptotic behaviours and determine the dynamics when the anisotropic principal pressures are proportional to the density. We expect distortions a…
In the context of GR, we study the thermodynamic stability of evolving Lorentzian wormholes at the apparent horizon. The average pressure of the anisotrropic components is considered as the pressure of the wormhole. According to the requirements of stable equilibrium in conventional thermodynamics, we calculate the heat capacity at constant pressure and Gibbs free energy and analyze the local and global thermodynamic stability of the wormhole.
Most of the observational claims in cosmology are based on the assumption that the universe is isotropic and homogeneous so they essentially test different types of Friedmann models. This also refers to recent observations of supernovae Ia, which, within the framework of Friedmann cosmologies give strong support to negative pressure matter and also weaken the age conflict. In this essay we drop the assumption of homogeneity, though temporarily leaving the assumption of isotropy with respect to one point, and show that supernovae data can be consistent with a model of the universe with inhomoge…
The existence of de-Sitter solutions and their stability within string theory became, in recent years, one of the central research questions within the string theory community. The so-called de-Sitter conjecture states that the de-Sitter vacua are unstable within string theory. Here, we study the de-Sitter solutions in string theory and their stability in the time direction using the $O(d,d)$ symmetry approach allowing for the calculation of the generic form of the string theory effective action. We study the undiscussed case of the constant generalized dilaton as well as the general form of d…
We study the stability of the isotropic vacuum Friedmann universe in gravity theories with higher-order curvature terms of the form $(R_{ab}R^{ab})^{n}$ added to the Einstein-Hilbert Lagrangian of general relativity on approach to an initial cosmological singularity. Earlier, we had shown that, when $% n=1$, a special isotropic vacuum solution exists which behaves like the radiation-dominated Friedmann universe and is stable to anisotropic and small inhomogeneous perturbations of scalar, vector and tensor type. This is completely different to the situation that holds in general relativity, whe…
We investigate the stability of self-gravitating spherically symmetric anisotropic spheres under radial perturbations. We consider both the Newtonian and the full general-relativistic perturbation treatment. In the general-relativistic case, we extend the variational formalism for spheres with isotropic pressure developed by Chandrasekhar. We find that, in general, when the tangential pressure is greater than the radial pressure, the stability of the anisotropic sphere is enhanced when compared to isotropic configurations. In particular, anisotropic spheres are found to be stable for smaller v…
We show the existence of an infinite family of finite-time singularities in isotropically expanding universes which obey the weak, strong, and dominant energy conditions. We show what new type of energy condition is needed to exclude them ab initio. We also determine the conditions under which finite-time future singularities can arise in a wide class of anisotropic cosmological models. New types of finite-time singularity are possible which are characterised by divergences in the time-rate of change of the anisotropic-pressure tensor. We investigate the conditions for the formation of finite-…
Radial stability of the continuous pressure gravastar is studied using the conventional Chandrasekhar method. The equation of state for the static gravastar solutions is derived and Einstein equations for small perturbations around the equilibrium are solved as an eigenvalue problem for radial pulsations. Within the model there exist a set of parameters leading to a stable fundamental mode, thus proving radial stability of the continuous pressure gravastar. It is also shown that the central energy density possesses an extremum in rho_c(R) curve which represents a splitting point between stable…
The stability of isotropic cosmological solutions in the Bianchi I model is considered. We prove that the stability of isotropic solutions in the Bianchi I metric for a positive Hubble parameter follows from their stability in the Friedmann-Robertson-Walker metric. This result is applied to models inspired by string field theory, which violate the null energy condition. Examples of stable isotropic solutions are presented. We also consider the k-essence model and analyse the stability of solutions of the form $Φ(t)=t$.
Anisotropic and isotropic slow-roll inflation supported by n-forms are sought. Canonical field strengths and their duals are taken into account, and they are allowed to have a potential and also, when necessary for slow-roll, a nonminimal curvature coupling. New isotropic solutions are found for three-forms. It is also shown that some n-form actions are equivalent to f(R) gravity and scalar field models with possible nonminimal couplings. Anisotropic solutions are found for two-forms, generalising vector inflation, however, also the two-form is unstable during inflation due to the nonminimal c…
We consider dynamics of a flat anisotropic Universe filled by a perfect fluid near a cosmological singularity in quadratic gravity. Two possible regimes are described -- the Kasner anisotropic solution and an isotropic "vacuum radiation" solution which has three sub cases depending on whether the equation of state parameter $w$ is bigger, smaller or equals to $1/3$. Initial conditions for numerical integrations have been chosen near General Relativity anisotropic solution with matter (Jacobs solution). We have found that for such initial conditions there is a range of values of coupling consta…
We investigate the turbulence effect in dark fluid universe with linear inhomogeneous equation of state. Attention is attached to two physical situations. First, we perform the perturbative analysis of turbulence and check its effects around the Big Rip. Later, treating the turbulence energy density as a part of total dark fluid, we study the stability of the system. The result shows that the stability is achieving as the energy density of turbulence decreases, changing into heat (the radiation), in perfect agreement with the avoidance of the Big Rip.
We study the Einstein equations of the static spherically symmetric anisotropic fluid system in curvature coordinates to find algorithms that generate all solutions and all solutions that are regular at the center. All possible combinations of input functions from the set of four functions that characterize the anisotropic system are considered and all equivalent conditions for central regularity are determined (for both isotropic and anisotropic systems). We provide the first regularity analysis of the known algorithm that uses the potential function and anisotropy as inputs. For three other …
The stability of isotropic cosmological solutions for two-field models in the Bianchi I metric is considered. We prove that the sufficient conditions for the Lyapunov stability in the Friedmann-Robertson-Walker metric provide the stability with respect to anisotropic perturbations in the Bianchi I metric and with respect to the cold dark matter energy density fluctuations. Sufficient conditions for the Lyapunov stability of the isotropic fixed points of the system of the Einstein equations have been found. We use the superpotential method to construct stable kink-type solutions and obtain suff…
Unitarity of evolution in gravitational collapses implies existence of macroscopic stable horizonless objects. With such objects in mind, we study the effects of anisotropy of pressures on the stability of stars. We consider stars in four or higher dimensions and also stars in M theory made up of (intersecting) branes. Taking the stars to be static, spherically symmetric and the equations of state to be linear, we study `singular solutions' and the asymptotic perturbations around them. Oscillatory perturbations are likely to imply instability. We find that non oscillatory perturbations, which …
We study anisotropic cosmologies of a scalar field interacting with an SU(2) gauge field via a gauge-kinetic coupling. We analyze Bianchi class A models, which include Bianchi type I, II, VI0, VII0, VIII and IX. The linear stability of isotropic inflationary solution with background magnetic field is shown, which generalizes the known results for U(1) gauge fields. We also study anisotropic inflationary solutions, all of which turn out to be unstable. Then nonlinear stability for the isotropic inflationary solution is examined by numerically investigating the dependence of the late-time behavi…
