An axially symmetric spacetime filled with an anisotropic fluid (original) (raw)

A static axisymmetric anisotropic fluid solution in general relativity

Astrophysics and Space Science, 1990

Einstein's interior field equations in general relativity are considered when spacetime is static and axisymmetric and the energy-momentum tensor represents an anisotropic fluid. After imposing a set of simplifying assumptions a two-parameter solution is derived and its properties are discussed. The solution is found to be physically reasonable in a certain range of the parameters in which case the metric could represent a core of anisotropie matter.

Relativistic Anisotropic Fluid Distributions in Equilibrium in General Relativity

Numerous models are developed by various researchers to describe the solution of the Einstein’s field equations when the matter is in the perfect fluid form. Thus we have many isotropic solutions to study. In this Paper, we find the anisotropic solutions of the Einstein’s field equations from the perfect fluid distributions. For that purpose, we have followed an algorithm suggested by Maharaj and Chaisi to generate anisotropic solutions for the seed isotropic metrics. Here, we have applied this algorithm to Schwarzschild exterior metric, Einstein’s static universe, Cosmological Solution found by Tikekar in 1970. Among these; the outcome of the last metric is the interesting one, as it gives the information regarding the super dense matter distributions. Practically we can think of the anisotropy in the super dense stars due to a very high pressure. Thus, we have provided the description of these four metrics when anisotropy evolved therein.

Anisotropic Fluid Distribution in Bimetric Theory of Relativity

Astrophysics and Space Science, 2004

In this paper we have presented a procedure to obtain exact analytical solutions of field equations for spherically symmetric self-gravitating distribution of anisotropic matter in bimetric theory of gravitation. The solution agrees with the Einstein's general relativity for a physical system compared to the size of universe such as the solar system.

A Cylindrically Symmetric and Static Anisotropic Fluid Spacetime and the Naked Singularity

Advances in High Energy Physics, 2018

A cylindrically symmetric and static solution of Einstein’s field equations was presented. The spacetime is conformally flat and regular everywhere except on the symmetry axis where it possesses a naked curvature singularity. The matter-energy source anisotropic fluids violate the weak energy condition (WEC) and diverge on the symmetry axis. We discuss geodesics motion of free test-particles near to the singularity, geodesic expansion in the metric to understand the nature of singularity which is naked or covered, and finally the C-energy of the spacetime.

AN EXACT SOLUTION OF EINSTEIN EQUATIONS FOR INTERIOR FIELD OF AN ANISOTROPIC FLUID SPHERE

In this paper, an anisotropic relativistic fluid sphere with variable density, which decreases along the radius and is maximum at the centre, is discussed. Spherically symmetric static space-time with spheroidal physical 3-space is considered. The source is an anisotropic fluid. The solution is an anisotropic generalization of the solution discussed by Vaidya and Tikekar [1]. The physical three space constant time has spheroidal solution. The line element of the solution can be expressed in the form Patel and Desai [2]. The material density is always positive. The solution efficiently matches with Schwarzschild exterior solution across the boundary. It is shown that the model is physically reasonable by studying the numerical estimates of various parameters. The density vs radial pressure relation in the interior is discussed numerically. An anisotropy effect on the redshift is also studied numerically.

Rotating Cylinders with Anisotropic Fluids in General Relativity

Gravitation and Cosmology

We consider anisotropic fluids with directional pressures p i = w i ρ (ρ is the density, w i = const, i = 1, 2, 3) as sources of gravity in stationary cylindrically symmetric space-times. We describe a general way of obtaining exact solutions with such sources, where the main features are splitting of the Ricci tensor into static and rotational parts and using the harmonic radial coordinate. Depending on the values of w i , it appears possible to obtain general or special solutions to the Einstein equations, thus recovering some known solutions and finding new ones. Three particular examples of exact solutions are briefly described: with a stiff isotropic perfect fluid (p = ρ), with a distribution of cosmic strings of azimuthal direction (i.e., forming circles around the z axis), and with a stationary combination of two opposite radiation flows along the z axis.

Inverse approach to Einstein’s equations for fluids with vanishing anisotropic stress tensor

Physical Review D, 2008

We expand previous work on an inverse approach to Einstein Field Equations where we include fluids with energy flux and consider the vanishing of the anisotropic stress tensor. We consider the approach using warped product spacetimes of class B1. Although restricted, these spacetimes include many exact solutions of interest to compact object studies and to cosmological models studies. The question explored here is as follows: given a spacetime metric, what fluid flow (timelike congruence), if any, could generate the spacetime via Einstein's equations. We calculate the flow from the condition of a vanishing anisotropic stress tensor and give results in terms of the metric functions in the three canonical types of coordinates. A condition for perfect fluid sources is also provided. The framework developed is algorithmic and suited for the study and validation of exact solutions using computer algebra systems. The framework can be applied to solutions in comoving and non-comoving frames of reference, and examples in different types of coordinates are worked out.

Axially Symmetric Perfect Fluid Cosmological Model in Modified Theory of Gravity

International Journal for Research in Applied Science & Engineering Technology (IJRASET), 2022

With an appropriate choice of the function f (R,T) , an anisotropic Axially Symmetric Space – time filled with perfect fluid in general relativity and also in the framework of f (R,T) gravity proposed by Harko et. al. (in arXiv: 1104. 2669 [grqc],2011) has been studied. The field equations have been solved by using the anisotropy features of the universe in Axially Symmetric Bianchi type- I Space – time. We have been discussed some physical properties of the models. We observed that the involvement of new function f (R,T) does not affect the geometry of the space-time but slightly changes the matter distribution.

Discussions on a special static spherically symmetric perfect fluid solution of Einstein's equations

2008

In this article, a special static spherically symmetric perfect fluid solution of Einstein's equations is provided. Though pressure and density both diverge at the origin, their ratio remains constant. The solution presented here fails to give positive pressure but nevertheless, it satisfies all energy conditions. In this new spacetime geometry, the metric becomes singular at some finite value of radial coordinate although, by using isotropic coordinates, this singularity could be avoided, as has been shown here. Some characteristics of this solution are also discussed.

Anisotropic Spheres in General Relativity

streaming.ictp.trieste.it

A prescription originally conceived for perfect fluids is extended to the case of anisotropic pressures. The method is used to obtain exact analytical solutions of the Einstein equations for spherically symmetric selfgravitating distribution of anisotropic matter. The solutions are matched to the Schwarzschild exterior metric.