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

2015 ◽  
Vol 04 (12) ◽  
pp. 280-285
Author(s):  
Lakshmi S. Desai .
Keyword(s):  
Exact Solution ◽  
Einstein Equations ◽  
Fluid Sphere ◽  
Anisotropic Fluid ◽  
Anisotropic Fluid Sphere

scholarly journals An Exact Model of an Anisotropic Relativistic Sphere

1995 ◽  
Vol 48 (4) ◽  
pp. 635 ◽  
Author(s):  
LK Patel ◽  
NP Mehta
Keyword(s):  
Exact Solution ◽  
General Relativity ◽  
Fluid Sphere ◽  
Anisotropic Fluid ◽  
Physical Parameters ◽  
Field Equations ◽  
Exterior Solution ◽  
Exact Model ◽  
Anisotropic Fluid Sphere

In this paper the field equations of general relativity are solved to obtain an exact solution for a static anisotropic fluid sphere. The solution is free from singularity and satisfies the necessary physical requirements. The physical 3-space of the solution is pseudo-spheroidal. The solution is matched at the boundary with the Schwarzschild exterior solution. Numerical estimates of various physical parameters are briefly discussed.

scholarly journals Mimicking static anisotropic fluid spheres in general relativity

2016 ◽  
Vol 25 (02) ◽  
pp. 1650019 ◽  
Author(s):  
Petarpa Boonserm ◽  
Tritos Ngampitipan ◽  
Matt Visser
Keyword(s):  
Electromagnetic Field ◽  
Scalar Field ◽  
Charge Density ◽  
Perfect Fluid ◽  
Radial Pressure ◽  
Energy Conditions ◽  
Fluid Sphere ◽  
Anisotropic Fluid ◽  
Spherically Symmetric ◽  
Anisotropic Fluid Sphere

We argue that an arbitrary general relativistic static anisotropic fluid sphere, (static and spherically symmetric but with transverse pressure not equal to radial pressure), can nevertheless be successfully mimicked by suitable linear combinations of theoretically attractive and quite simple classical matter: a classical (charged) isotropic perfect fluid, a classical electromagnetic field and a classical (minimally coupled) scalar field. While the most general decomposition is not unique, a preferred minimal decomposition can be constructed that is unique. We show how the classical energy conditions for the anisotropic fluid sphere can be related to energy conditions for the isotropic perfect fluid, electromagnetic field, and scalar field components of the model. Furthermore, we show how this decomposition relates to the distribution of both electric charge density and scalar charge density throughout the model. The generalized TOV equation implies that the perfect fluid component in this model is automatically in internal equilibrium, with pressure forces, electric forces, and scalar forces balancing the gravitational pseudo-force. Consequently, we can build theoretically attractive matter models that can be used to mimic almost any static spherically symmetric spacetime.

scholarly journals Vacuum solutions of Einstein equations that depend on one coordinate

2020 ◽  
pp. 10-11
Author(s):  
S. Parnovsky
Keyword(s):  
Exact Solution ◽  
General Theory ◽  
Cosmological Constant ◽  
Gravitational Wave ◽  
Einstein Equations ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Vacuum Metrics ◽  
Vacuum Solutions ◽  
Zero Frequency

In the famous textbook written by Landau and Lifshitz all the vacuum metrics of the general theory of relativity are derived, which depend on one coordinate in the absence of a cosmological constant. Unfortunately, when considering these solutions the authors missed some of the possible solutions discussed in this article. An exact solution is demonstrated, which is absent in the book by Landau and Lifshitz. It describes space-time with a gravitational wave of zero frequency. It is shown that there are no other solutions of this type than listed above and Minkowski’s metrics. The list of vacuum metrics that depend on one coordinate is not complete without solution provided in this paper.

scholarly journals Regularity condition on the anisotropy induced by gravitational decoupling in the framework of MGD

2020 ◽  
Vol 80 (2) ◽  
Author(s):  
G. Abellán ◽  
V. A. Torres-Sánchez ◽  
E. Fuenmayor ◽  
E. Contreras
Keyword(s):  
Standard Method ◽  
Regularity Condition ◽  
Physical Characteristics ◽  
Compact Objects ◽  
Anisotropy Factor ◽  
Einstein Equations ◽  
Anisotropic Fluid ◽  
Acceptable Solution ◽  
Geometric Deformation ◽  
Deformation Approach

Abstract We use gravitational decoupling to establish a connection between the minimal geometric deformation approach and the standard method for obtaining anisotropic fluid solutions. Motivated by the relations that appear in the framework of minimal geometric deformation, we give an anisotropy factor that allows us to solve the quasi–Einstein equations associated to the decoupling sector. We illustrate this by building an anisotropic extension of the well known Tolman IV solution, providing in this way an exact and physically acceptable solution that represents the behavior of compact objects. We show that, in this way, it is not necessary to use the usual mimic constraint conditions. Our solution is free from physical and geometrical singularities, as expected. We have presented the main physical characteristics of our solution both analytically and graphically and verified the viability of the solution obtained by studying the usual criteria of physical acceptability.

scholarly journals Einsteinian Gravitational Field of a Heterogeneous Fluid Sphere

1925 ◽  
Vol 44 ◽  
pp. 72-78
Author(s):  
Jyotirmaya Ghosh
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Empty Space ◽  
Variable Coefficients ◽  
Fluid Sphere ◽  
Uniform Density ◽  
Large Radius ◽  
Field Equations ◽  
Linear Differential ◽  
Gravitational Equations

The field-equations of gravitation in Einstein's theory have been solved in the case of an empty space, giving rise to de Sitter's spherical world. In the case of homogeneous matter filling all space, the solution gives Einstein's cylindrical world. The field corresponding to an isolated particle has been obtained by Schwarzchild. He has also obtained a solution for a fluid sphere with uniform density, a problem treated also by Nordström and de Donder. A new solution of the gravitational equations has been obtained in this paper, which corresponds to the field of a heterogeneous fluid sphere, the density at any point being a certain function of the distance of the point from the centre. The law of density is quite simple and such as to give finite density at the centre and gradually diminishing values as the distance from the centre increases, as might be expected of a natural sphere of fluid of large radius. The general problem of the fluid sphere with any arbitrary law of density cannot be solved in exact terms. It will be seen, however, from a theorem obtained in this paper, that the solution depends on a linear differential equation of the second order with variable coefficients involving the density, and thus the laws of density for which the problem admits of exact solution are those for which the above coefficients satisfy the conditions of integrability of the differential equation. An approximate solution for any law of density may be obtained by the method of series.

scholarly journals Modelling of a compact anisotropic star as an anisotropic fluid sphere in f(T) gravity

2018 ◽  
Vol 96 (12) ◽  
pp. 1295-1303 ◽  
Author(s):  
D. Momeni ◽  
G. Abbas ◽  
S. Qaisar ◽  
Zaid Zaz ◽  
R. Myrzakulov
Keyword(s):  
Anisotropic Fluid ◽  
Physical Parameters ◽  
Parametric Form ◽  
Dynamical Equations ◽  
Strange Stars ◽  
Exact Model ◽  
Anisotropic Fluid Sphere ◽  
Metric Functions ◽  
Anisotropic Stars ◽  
Anisotropic Star

In this article, the authors have discussed a new exact model of anisotropic stars in the f(T) theory of gravity. A parametric form of the metric functions has been implemented to solve the dynamical equations in f(T) theory with the anisotropic fluid. The novelty of the work is that the obtained solutions do not contain singularity but are potentially stable. The estimated values for mass and radius of the different strange stars, RX J 1856–37, Her X-1, and Vela X-12, have been utilized to find the values of unknown constants in Krori and Barua metrics. The physical parameters like anisotropy, stability, and redshift of the stars have been examined in detail.

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