Static Anisotropic Solutions to Einstein Equation with a Nonlocal Equation of State (original) (raw)

Static Anisotropic Solutions to Einstein Equations with a Nonlocal Equation of State

Eprint Arxiv Gr Qc 0012019, 2000

We present a general method to obtain static anisotropic spherically symmetric solutions, satisfying a nonlocal equation of state, from known density profiles. This equation of state describes, at a given point, the components of the corresponding energy-momentum tensor not only as a function at that point, but as a functional throughout the enclosed configuration. In order to establish the physical aceptability of the proposed static family of solutions satisfying nonlocal equation of state,\textit{}we study the consequences imposed by the junction and energy conditions for anisotropic fluids in bounded matter distribution. It is shown that a general relativistic spherically symmetric bounded distributions of matter, at least for certain regions, could satisfy a nonlocal equation of state.

Nonlocal equation of state in anisotropic static fluid spheres in general relativity

Can J Phys, 2004

We show that it is possible to obtain, at least certain regions within spherically symmetric static matter configurations, credible anisotropic fluids satisfying a nonlocal equation of state. This particular type of equation of state provides, at a given point, the radial pressure not only as a function of the density at that point, but its functional throughout the enclosed distribution. To establish the physical plausibility of the proposed family of solutions satisfying a nonlocal equation of state, we study the constraints imposed by the junction, energy, and some intuitive physical conditions. We show that these static fluids having this particular equation of state are "naturally" anisotropic in the sense that they satisfy, identically, the anisotropic Tolman-Oppenheimer-Volkov equation. We also show that it is possible to obtain physically plausible static anisotropic spherically symmetric matter configurations starting from known density profiles, and also for configurations where tangential pressures vanish. This very particular type of relativistic sphere with vanishing tangential stresses is inspired by some of the models proposed to describe extremely magnetized neutron stars (magnetars) during the transverse quantum collapse.

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.

Relativistic anisotropic fluid spheres satisfying a non-linear equation of state

The European Physical Journal C, 80(5): 371, 2020

In this work, a spherically symmetric and static relativistic anisotropic fluid sphere solution of the Einstein field equations is provided. To build this particular model, we have imposed metric potential e 2λ(r) and an equation of state. Specifically, the so-called modified generalized Chap-lygin equation of state with ω = 1 and depending on two parameters, namely, A and B. These ingredients close the problem, at least mathematically. However, to check the feasibility of the model, a complete physical analysis has been performed. Thus, we analyze the obtained geometry and the main physical observables, such as the density ρ, the radial p r , and tangential p t pressures as well as the anisotropy factor . Besides, the stability of the system has been checked by means of the velocities of the pressure waves and the rel-ativistic adiabatic index. It is found that the configuration is stable in considering the adiabatic index criteria and is under hydrostatic balance. Finally, to mimic a realistic compact object, we have imposed the radius to be R = 9.5 [km]. With this information and taking different values of the parameter A the total mass of the object has been determined. The resulting numerical values for the principal variables of the model established that the structure could represent a quark (strange) star mixed with dark energy.

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.

Anisotropic static spheres with linear equation of state in isotropic coordinates

Astrophysics and Space Science, 2015

In this paper we present a general framework for generating exact solutions to the Einstein field equations for static, anisotropic fluid spheres in comoving, isotropic coordinates obeying a linear equation of state of the form p r = αρ − β. We show that all possible solutions can be obtained via a single generating function defined in terms of one of the gravitational potentials. The physical viability of our solution-generating method is illustrated by modeling a static fluid sphere describing a strange star.

Non-local equation of state in general relativistic radiating spheres

Class Quantum Gravity, 1999

We show that under particular circumstances a general relativistic spherically symmetric bounded distribution of matter could satisfy a non-local equation of state. This equation describes, at a given point, the components of the corresponding energy-momentum tensor not only as a function at that point, but as a functional throughout the enclosed configuration. We have found that these types of dynamic bounded matter configurations, with constant compactness or gravitational potentials at the surface, admit a conformal Killing vector field and fulfil the energy conditions for anisotropic imperfect fluids. We present several analytical and numerical models satisfying these equations of state which collapse as reasonable radiating anisotropic spheres in general relativity.

Plausible families of compact objects with a nonlocal equation of state

Canadian Journal of Physics, 2013

We present the plausibility of some models emerging from an algorithm devised to generate a one-parameter family of interior solutions for the Einstein equations. We explore how their physical variables change as the family parameter varies. The models studied correspond to anisotropic spherical matter configurations having a nonlocal equation of state. This particular type of equation of state, with no causality problems, provides at a given point the radial pressure not only as a function of the density but as a functional of the enclosed matter distribution. We have found that there are several model-independent tendencies as the parameter increases: the equation of state tends to be stiffer and the total mass becomes half of its external radius. Profiting from the concept of cracking of materials in general relativity, we obtain that these models become more potentially stable as the family parameter increases.

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.