Symmetric Perfect Fluid Spacetimes Research Articles

Perfect fluid locally rotationally symmetric Bianchi Type-I spacetimes admitting concircular vector fields in f(T) gravity

We obtained the solutions of Einstein’s Field Equations (EFEs) for locally rotationally symmetric (LRS) Bianchi type-I perfect fluid spacetimes through the concircular vector fields (CCVFs) in [Formula: see text] gravity. It is shown that such metrics admit CCVFs of 4, 5, 6, 7, 8 and 15 dimensions. We also calculated the energy density, fluid pressure, torsion scalar [Formula: see text] and the form of the function [Formula: see text]. We did not specify the form of [Formula: see text] for the solution of EFEs but found a particular form of [Formula: see text] during the process of finding the CCVFs. It is observed that energy density and fluid pressure of some solutions are related as [Formula: see text], which means that the universe represented by these spacetime metrics behaves like dark energy models. For other solutions, it is observed that the fluid pressure and energy density can remain positive for particular choices of the constants involved. Thus, in these cases the rate of expansion can slow down due to positive attractive effect. We also calculated the Hubble’s parameter ([Formula: see text]), scalar expansion ([Formula: see text]), shear scalar ([Formula: see text]), anisotropy parameter ([Formula: see text]) and the deceleration parameter ([Formula: see text]) associated with each of the obtained exact LRS Bianchi type-I solutions. It is observed that the physical behavior of the spacetime changes with the number of admitting CCVFs. A constant anisotropic behavior for 15-dimensional CCVFs is observed to change to isotropic nature for seven-dimensional CCVFs.

Some curvature properties of perfect fluid spacetimes

In this paper we assume that a perfect fluid is the source of the gravitational field while analyzing the solutions to the Einstein field equations. With this new and innovative approach, we investigate some curvature properties of perfect fluid spacetimes. Firstly, we provide a necessary condition for a Lorentzian manifold to be a perfect fluid spacetime. We prove that a conformally flat perfect fluid space-time is a spacetime of quasi constant sectional curvature. Also, we acquire that a conharmonically flat perfect fluid spacetime represents the radiation era. Next, we show that if a stiff matter fluid obeys Yang’s equations, then the vorticity of the fluid vanishes. Moreover, we find that if the Ricci tensor is Killing, then the perfect fluid spacetime is (i) expansion-free and shear-free, and its flow is geodesic, however, not necessarily vorticity-free, and (ii) σ and p are constant. Besides, we establish that Ricci semi-symmetric or Ricci symmetric perfect fluid spacetimes represent either dark matter era, or phantom era. Finally, we acquire that if a perfect fluid is Ricci symmetric, then either the spacetime represents a dark matter era, or a static spacetime.

A note on concircular vector fields of static plane symmetric perfect fluid spacetimes in f(T) theory of gravity

A note on concircular vector fields of static plane symmetric perfect fluid spacetimes in f(T) theory of gravity

Classification of static spherically symmetric perfect fluid space-times via conformal vector fields in f(T) gravity

In this paper, we classify static spherically symmetric (SS) perfect fluid space-times via conformal vector fields (CVFs) in f(T) gravity. For this analysis, we first explore static SS solutions by solving the Einstein field equations in f(T) gravity. Secondly, we implement a direct integration technique to classify the resulting solutions. During the classification, there arose 20 cases. Studying each case thoroughly, we came to know that in three cases the space-times under consideration admit proper CVFs in f(T) gravity. In one case, the space-time admits proper homothetic vector fields, whereas in the remaining 16 cases either the space-times become conformally flat or they admit Killing vector fields.

Almost pseudo-Ricci symmetric spacetime solutions in F(R)-gravity

The objective of the present paper is to study 4-dimensional almost pseudo Ricci symmetric perfect fluid spacetimes $$(\textit{APRS})_4$$ . We show that a Robertson–Walker spacetime is $$(\textit{APRS})_4$$ and vice versa under certain condition imposed on its scale factor. Some popular toy models of F(R)-gravity are also studied under the current setting and various energy conditions are investigated.

Conformal vector fields of static spherically symmetric perfect fluid space-times in modified teleparallel theory of gravity

In this paper, initially we solve the Einstein field equations (EFEs) for a static spherically (SS) symmetric perfect fluid space-times in the [Formula: see text] gravity with the aid of some algebraic techniques. The extracted solutions are then utilized in order to get conformal vector fields (CVFs). It is important to mention that the adopted techniques enable us to obtain various classes of space-times with viable [Formula: see text] gravity models which already exist in the literature. Excluding all such classes, we find that there exist three cases for which the space-times admit proper CVFs, whereas in rest of the cases, CVFs become KVFs. We have also highlighted some physical implications of our obtained results.

Classification of proper non-static cylindrically symmetric perfect fluid space-times via conformal vector fields in f(R) gravity

In this paper, we classify proper non-static cylindrically symmetric (CS) perfect fluid space-times via conformal vector fields (CVFs) in the [Formula: see text] gravity. In order to classify the space-times, we use the algebraic and direct integration approaches. In the process of classification, there exist 23 cases for which the considered space-times become proper non-static. By studying each case in detail, we find that the conformal vector fields are of dimensions two, three and fifteen in the [Formula: see text] gravity.

A note on classification of static plane symmetric perfect fluid space-times via proper conformal vector fields in f(G) theory of gravity

In the [Formula: see text] theory of gravity, we classify static plane symmetric perfect fluid space-times via proper conformal vector fields (CVFs) using algebraic and direct integration approaches. During this classification, we found eight cases. Studying each case in detail, we found that the dimensions of CVFs are 4, 5, 6 or 15. In the cases when the space-time admits 15 independent CVFs it becomes conformally flat.

C3 matching for asymptotically flat spacetimes

We propose a criterion for finding the minimum distance at which an interior solution of Einstein’s equations can be matched with an exterior asymptotically flat solution. The location of the matching hypersurface is thus constrained by a criterion defined in terms of the eigenvalues of the Riemann curvature tensor by using repulsive gravity effects. To determine the location of the matching hypersurface, we use the first derivatives of the curvature eigenvalues, implying C3 differentiability conditions. The matching itself is performed by demanding continuity of the curvature eigenvalues across the matching surface. We apply the C3 matching approach to spherically symmetric perfect fluid spacetimes and obtain the physically meaningful condition that density and pressure should vanish on the matching surface. Several perfect fluid solutions in Newton and Einstein gravity are tested.

Согласование условий для внутреннего и внешнего пространства-времени астрофизических компактных объектов

We study the problem of matching the interior and exterior solutions of Einstein’s equations for astrophysical compact objects. We propose a criterion for finding the minimum distance at which an interior solution of Einstein’s equations can be matched with an exterior asymptotically flat solution. The location of the matching hypersurface is thus constrained by a criterion defined in terms of the eigenvalues of the Riemann curvature tensor by using repulsive gravity effects. We propose a C3 matching which consists in demanding that the derivatives of a particular curvature eigenvalue are smooth on the matching hypersurface. We apply the C3 matching approach to spherically symmetric perfect fluid spacetimes and obtain the physically meaningful condition that density and pressure should vanish on the matching surface. As aresult we obtain a minimum radius at which the matching can be carried out and a fixed value for the pressure on the symmetry axis.  These values are then used to reach the smooth matching of the interior and exterior metric functions. Several perfect fluid solutions in Newton gravity are tested.

Generating static perfect-fluid solutions of Einstein’s equations

We present a method for generating exact interior solutions of Einstein’s equations in the case of static and axially symmetric perfect-fluid spacetimes. The method is based upon a transformation that involves the metric functions as well as the density and pressure of the seed solution. In the limiting vacuum case, it reduces to the Zipoy-Voorhees transformation that can be used to generate metrics with multipole moments. All the metric functions of the new solution can be calculated explicitly from the seed solution in a simple manner. The physical properties of the resulting new solutions are shown to be completely different from those of the seed solution.

ALGORITHMIC CONSTRUCTION OF EXACT SOLUTIONS FOR NEUTRAL STATIC PERFECT FLUID SPHERES

Although it ranks amongst the oldest of problems in classical general relativity, the challenge of finding new exact solutions for spherically symmetric perfect fluid spacetimes is still ongoing because of a paucity of solutions which exhibit the necessary qualitative features compatible with observational evidence. The problem amounts to solving a system of three partial differential equations in four variables, which means that any one of four geometric or dynamical quantities must be specified at the outset and the others should follow by integration. The condition of pressure isotropy yields a differential equation that may be interpreted as second-order in one of the space variables or also as first-order Ricatti type in the other space variable. This second option has been fruitful in allowing us to construct an algorithm to generate a complete solution to the Einstein field equations once a geometric variable is specified ab initio. We then demonstrate the construction of previously unreported solutions and examine these for physical plausibility as candidates to represent real matter. In particular we demand positive definiteness of pressure, density as well as a subluminal sound speed. Additionally, we require the existence of a hypersurface of vanishing pressure to identify a radius for the closed distribution of fluid. Finally, we examine the energy conditions. We exhibit models which display all of these elementary physical requirements.

Thermodynamics of magnetized binary compact objects

Binary systems of compact objects with electromagnetic field are modeled by helically symmetric Einstein-Maxwell spacetimes with charged and magnetized perfect fluids. Previously derived thermodynamic laws for helically symmetric perfect-fluid spacetimes are extended to include the electromagnetic fields, and electric currents and charges; the first law is written as a relation between the change in the asymptotic Noether charge $\ensuremath{\delta}Q$ and the changes in the area and electric charge of black holes, and in the vorticity, baryon rest mass, entropy, charge and magnetic flux of the magnetized fluid. Using the conservation laws of the circulation of magnetized flow found by Bekenstein and Oron for the ideal magnetohydrodynamic fluid, and also for the flow with zero conducting current, we show that, for nearby equilibria that conserve the quantities mentioned above, the relation $\ensuremath{\delta}Q=0$ is satisfied. We also discuss a formulation for computing numerical solutions of magnetized binary compact objects in equilibrium with emphasis on a first integral of the ideal magnetohydrodynamic-Euler equation.

Separating expansion from contraction in spherically symmetric models with a perfect fluid: Generalization of the Tolman-Oppenheimer-Volkoff condition and application to models with a cosmological constant

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 allow its global validity. We analyze the particular cases of the Lema\^itre-Tolman-Bondi dust models with a cosmological constant as an example of a cold dark matter model with a cosmological constant (\Lambda-CDM) and its generalization to contain a central perfect-fluid core. These models provide simple, but physically interesting illustrations of our results.

Bianchi type-II space-times with constant deceleration parameter in self creation cosmology

The properties of locally rotationally symmetric Bianchi type-II perfect fluid space-times are analyzed in Barber’s second self-creation theory by using a special law of variation for Hubble’s parameter that yields a constant value of deceleration parameter. By assuming the equation of state p=γρ, many new solutions are obtained for different era—Zel’dovich, radiation, vacuum and vacuum energy dominated. The solutions with power-law and exponential expansion are discussed. A detailed study of geometrical and physical parameters is carried out. The nature of singularity is also clarified in each case.

Rotating perfect fluids in (2+1)-dimensional Einstein gravity

Stationary rotationally symmetric perfect fluid spacetimes are studied. We formulate the Einstein equations with a cosmological constant in a corotating Lorentz triad, and all stationary symmetric perfect fluid solutions to 2+1 Einstein gravity are derived. Stationary spacetimes containing perfect fluids with a constant energy density and a linear or a polytropic barotropic equation of state are explicitly shown. All known static circularly symmetric perfect fluid spacetimes can be obtained from the here derived stationary cosmological perfect fluid solutions.

Integrability analysis of a conformal equation in relativity

In 1987 C. C. Dyer, G. C. McVittie, and L. M. Oattes derived the (two) field equations for shear-free, spherically symmetric perfect fluid spacetimes which admit a conformai symmetry. We use the techniques of the Lie and Painleve analyses of differential equations to find solutions of these equations. The concept of a pseudo-partial Painleve property is introduced for the first time which could assist in finding solutions to equations that do not possess the Painleve property. The pseudo-partial Painleve property throws light on the distinction between the classes of solutions found independently by P. Havas and M. Wyman. We find a solution for all values of a particular parameter for the first field equation and link it to the solution of the second equation. We indicate why we believe that the first field equation cannot be solved in general. Both techniques produce similar results and demonstrate the close relationship between the Lie and Painleve analyses. We also show that both of the field equations of Dyeret al. may be reduced to the same Emden-Fowler equation of index two.

A geometric theory of shell singularities

We introduce and give the motivation for the concept of shell singularities. Shell singularities are a generalization of shell crossing singularities to spacetimes which are not necessarily spherically symmetric. We give a definition of strong cosmic censorship for shell singularities and show under which conditions shell singularities are censored. We study pregeodesics and geodesics which cross a shell singularity and introduce coordinates which are adapted to the singularity. We then specialize to spherical symmetry and discuss the family of perfect fluid spacetimes with shell crossing singularities given by Müller zum Hagen et al. We prove that spherically symmetric perfect fluid spacetimes with shell singularity have vanishing velocity of sound at the singularity. This lends further support to cosmic censorship.

Cosmic censorship in spherically symmetric perfect fluid spacetimes

The author shows that shell (crossing) singularities are at least marginally trapped, if the ratio of pressure and energy density tends to a nonzero constant for diverging energy density. This result gives strong support for weak cosmic censorship of shell crossing singularities, if a perfect fluid with physically realistic equations of state is considered.

Spherically symmetric spacetimes in the context of the compacted spin coefficient formalism

The equations governing the geometry of spherically symmetric spacetimes, are written in a coordinate independent way in the context of the compacted spin coefficient formalism. The necessary and sufficient conditions in order that a spherically symmetric spacetime admits a Killing vector or a Killing tensor orthogonal to the spherical group orbits are given. In the same context, the equations describing static and spherically symmetric perfect fluid spacetimes are also given.