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.
Spherically symmetric dissipative anisotropic fluids: A general study
Physical Review D, 2004
The full set of equations governing the evolution of self-gravitating spherically symmetric dissipative fluids with anisotropic stresses is deployed and used to carry out a general study on the behavior of such systems, in the context of general relativity. Emphasis is given to the link between the Weyl tensor, the shear tensor, the anisotropy of the pressure, and the density inhomogeneity. In particular we provide the general, necessary, and sufficient condition for the vanishing of the spatial gradients of energy density, which in turn suggests a possible definition of a gravitational arrow of time. Some solutions are also exhibited to illustrate the discussion.
The European Physical Journal C
We present an algorithm to generalize a plethora of well-known solutions to Einstein field equations describing spherically symmetric relativistic fluid spheres by relaxing the pressure isotropy condition on the system. By suitably fixing the model parameters in our formulation, we generate closed-form solutions which may be treated as an anisotropic generalization of a large class of solutions describing isotropic fluid spheres. From the resultant solutions, a particular solution is taken up to show its physical acceptability. Making use of the current estimate of mass and radius of a known pulsar, the effects of anisotropic stress on the gross physical behaviour of a relativistic compact star is also highlighted.
Black hole in closed spacetime with an anisotropic fluid
Physical Review D, 2017
We study spherically symmetric geometries made of anisotropic perfect fluid based on general relativity. The purpose of the work is to find and classify black hole solutions in closed spacetime. In a general setting, we find that a static and closed space exists only when the radial pressure is negative but its size is smaller than the density. The Einstein equation is eventually casted into a first order autonomous equation on two-dimensional plane of scale-invariant variables, which are equivalent to the Tolman-Oppenheimer-Volkoff (TOV) equation in general relativity. Then, we display various solution curves numerically. An exact solution describing a black hole solution in a closed spacetime was known in Ref. [1], which solution bears a naked singularity and negative energy era. We find that the two deficits can be remedied when ρ + 3p1 > 0 and ρ + p1 + 2p2 < 0, where the second violates the strong energy condition.
Some Results on the Integrability of Einstein's Field Equations for Axistationary Perfect Fluids
The Ninth Marcel Grossmann Meeting, 2002
Using an orthonormal Lorentz frame approach to axistationary perfect fluid spacetimes, we have formulated the necessary and sufficient equations as a first order system, and investigated the integrability conditions of this set of equations. The integrability conditions are helpful tools when it comes to check the consequences and/or compatibility of certain simplifying assumptions, e.g. Petrov types. Furthermore, using this method, a relation between the fluid shear and vorticity is found for barotropic fluids. We collect some results concerning Petrov types, and it is found that an incompressible axistationary perfect fluid must be of Petrov type I.
Plane symmetric self-gravitating fluids with pressure equal to energy density
Communications in Mathematical Physics, 1973
Solutions of the Cauchy problem associated with the Einstein field equations which satisfy general initial conditions are obtained under the assumptions that (1) the source of the gravitational field is a perfect fluid with pressure, p, equal to energy density, w, and (2) the space-time admits the three parameter group of motions of the Euclidean plane, that is, the space-time is plane symmetric. The results apply to the situation where the source of the gravitational field is a massless scalar field since such a source has the same stress-energy tensor as an irrotational fluid with p = w. The relation between characteristic coordinates and comoving ones is discussed and used to interpret a number of special solutions. A solution involving a shock wave is discussed.
Applying the method of conformal metric to a given static axially symmetric vacuum solution of the Einstein equations, we have shown that there is no solution representing a cosmic ideal fluid which is asymtotically FLRW. Letting the cosmic fluid to be imperfect there are axially symmetric solutions tending to FLRW at space infinity. The solution we have found represents an axially symmetric spacetime leading to a spherically symmetric Einstein tensor. Therefore, we have found a solution of Einstein equations representing a spherically symmetric matter distribution corresponding to a spacetime which does not reflect the same symmetry. We have also found another solution of Einstein equation corresponding to the same energy tensor with spherical symmetry.
A new solution of embedding class I representing anisotropic fluid sphere in general relativity
In this paper, we are willing to develop a model of an anisotropic star by choosing a 24 new grr metric potential. All the physical parameters like the matter density, radial and 25 transverse pressure are regular inside the anisotropic star, with the speed of sound less 26 than the speed of light. So the new solution obtained by us gives satisfactory descrip-27 tion of realistic astrophysical compact stars. The model of this paper is compatible 28 with observational data of compact objects like RX J1856-37, Her X-1, Vela X-12 and 29 Cen X-3. A particular model of Her X-1 (Mass 0.98 M and radius = 6.7 km.) is stud-30 ied in detail and found that it satisfies all the condition needed for physically accept-31 able model. Our model is described analytically as well as with the help of graphical 32 representation. 33
Multidimensional cosmology with anisotropic fluid: acceleration and variation of G
Gravitation and Cosmology
A multidimensional cosmological model describing the dynamics of n+1 Ricci-flat factor-spaces M_i in the presence of a one-component anisotropic fluid is considered. The pressures in all spaces are proportional to the density: p_i = w_i \rho, i = 0,...,n. Solutions with accelerated expansion of our 3-space M_0 and small enough variation of the gravitational constant G are found. These solutions exist for two branches of the parameter w_0. The first branch describes superstiff matter with w_0 > 1, the second one may contain phantom matter with w_0 < - 1, e.g., when G grows with time.