An exact solution of the Einstein field equations for a static electrically charged anisotropic fluid sphere

2000 ◽  
Author(s):  
Lau Loi So
Keyword(s):  
Exact Solution ◽  
Fluid Sphere ◽  
Anisotropic Fluid ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Anisotropic Fluid Sphere ◽  
Electrically Charged

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.

ANISOTROPIC SELF-SIMILAR COSMOLOGICAL MODEL WITH DARK ENERGY

2006 ◽  
Vol 15 (07) ◽  
pp. 991-999 ◽  
Author(s):  
P. R. PEREIRA ◽  
M. F. A. DA SILVA ◽  
R. CHAN
Keyword(s):  
Dark Energy ◽  
Energy Conditions ◽  
Anisotropic Fluid ◽  
Accelerating Universe ◽  
Spherically Symmetric ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Self Similarity ◽  
Normal Matter ◽  
Self Similar

We study space–times having spherically symmetric anisotropic fluid with self-similarity of zeroth kind. We find a class of solutions to the Einstein field equations by assuming a shear-free metric and that the fluid moves along time-like geodesics. The energy conditions, and geometrical and physical properties of the solutions are studied and we find that it can be considered as representing an accelerating universe. At the beginning all the energy conditions were fulfilled but beyond a certain time (a maximum geometrical radius) none of them is satisfied, characterizing a transition from normal matter (dark matter, baryon matter and radiation) to dark energy.

scholarly journals Emergence of a cosmological constant in anisotropic fluid cosmology

2021 ◽  
pp. 2150156
Author(s):  
M. Cadoni ◽  
A. P. Sanna
Keyword(s):  
Cosmological Constant ◽  
Large Scale ◽  
Spatial Scales ◽  
Time Dependent ◽  
Anisotropic Fluid ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Coincidence Problem ◽  
Order Of Magnitude ◽  
Natural Way

In this paper, we investigate anisotropic fluid cosmology in a situation where the space–time metric back-reacts in a local, time-dependent way to the presence of inhomogeneities. We derive exact solutions to the Einstein field equations describing Friedmann–Lemaítre–Robertson–Walker (FLRW) large-scale cosmological evolution in the presence of local inhomogeneities and time-dependent backreaction. We use our derivation to tackle the cosmological constant problem. A cosmological constant emerges by averaging the backreaction term on spatial scales of the order of 100 Mpc, at which our universe begins to appear homogeneous and isotropic. We find that the order of magnitude of the “emerged” cosmological constant agrees with astrophysical observations and is related in a natural way to baryonic matter density. Thus, there is no coincidence problem in our framework.

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.

Anisotropic fluid spheres satisfying the Karmarkar condition

2019 ◽  
Vol 34 (15) ◽  
pp. 1950113 ◽  
Author(s):  
Nayan Sarkar ◽  
Susmita Sarkar ◽  
Farook Rahaman ◽  
Ksh. Newton Singh ◽  
Hasrat Hussain Shah
Keyword(s):  
Compact Stars ◽  
Anisotropic Fluid ◽  
Stability Factor ◽  
Spherically Symmetric ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Suitable Form ◽  
Fluid Spheres ◽  
Interior Solutions ◽  
Tov Equation

In this paper, we present new physically viable interior solutions of the Einstein field equations for static and spherically symmetric anisotropic compact stars satisfying the Karmarkar condition. For presenting the exact solutions, we provide a new suitable form of one of the metric potential functions. Obtained solutions satisfy all the physically acceptable properties of realistic fluid spheres and hence solutions are well-behaved and representing matter distributions are in equilibrium state and potentially stable by satisfying the TOV equation and the condition on stability factor, adiabatic indices. We analyze the solutions for two well-known compact stars Vela X-1 (Mass = 1.77 M[Formula: see text], R = 9.56 km) and Cen X-3 (Mass = 1.49 M[Formula: see text], R = 9.17 km).

COLLAPSING FLUID WITH SELF-SIMILARITY OF THE SECOND KIND IN 2 + 1 GRAVITY

2008 ◽  
Vol 17 (05) ◽  
pp. 725-735 ◽  
Author(s):  
M. R. MARTINS ◽  
M. F. A. DA SILVA ◽  
YUMEI WU
Keyword(s):  
Dimensional Space ◽  
Radial Pressure ◽  
Anisotropic Fluid ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Self Similarity ◽  
Naked Singularities ◽  
Circular Symmetry ◽  
Global Properties ◽  
Dust Fluid

Anisotropic fluid with self-similarity of the second kind in (2 + 1)-dimensional space–times with circular symmetry is studied. By imposing the condition that the radial pressure vanishes, we show that the only allowed solutions are the ones that represent dust fluid. All such solutions to the Einstein field equations are found and their local and global properties are studied in detail. It is found that some can be interpreted as representing gravitational collapse, in which both naked singularities and black holes can be formed.

GRAVITATIONAL COLLAPSE OF AN ANISOTROPIC FLUID WITH SELF-SIMILARITY OF THE SECOND KIND

2006 ◽  
Vol 15 (09) ◽  
pp. 1407-1417 ◽  
Author(s):  
C. F. C. BRANDT ◽  
R. CHAN ◽  
M. F. A. DA SILVA ◽  
JAIME F. VILLAS DA ROCHA
Keyword(s):  
Black Hole ◽  
Naked Singularity ◽  
Radial Pressure ◽  
The Self ◽  
Energy Conditions ◽  
Anisotropic Fluid ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Self Similarity ◽  
Self Similar

We study the evolution of an anisotropic fluid with kinematic self-similarity of the second kind. We found a class of solution to the Einstein field equations by assuming an equation of state where the radial pressure of the fluid is proportional to its energy density (pr = ωρ) and that the fluid moves along time-like geodesics. The self-similarity requires ω = -1. The energy conditions, geometrical and physical properties of the solutions are studied. We have found that, depending on the self-similar parameter α, they may represent a black hole or a naked singularity.

GRAVITATIONAL COLLAPSE OF SPHERICALLY SYMMETRIC ANISOTROPIC FLUID WITH HOMOTHETIC SELF-SIMILARITY

2003 ◽  
Vol 12 (07) ◽  
pp. 1315-1332 ◽  
Author(s):  
C. F. C. BRANDT ◽  
M. F. A. DA SILVA ◽  
JAIME F. VILLAS DA ROCHA ◽  
R. CHAN
Keyword(s):  
Physical Properties ◽  
Gravitational Collapse ◽  
Energy Conditions ◽  
Anisotropic Fluid ◽  
Spherically Symmetric ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Self Similarity ◽  
Tangential Pressure

We study spacetimes of spherically symmetric anisotropic fluid with homothetic self-similarity. We find a class of solutions to the Einstein field equations by assuming that the tangential pressure of the fluid is proportional to its radial one and that the fluid moves along time-like geodesics. The energy conditions, and geometrical and physical properties of these solutions are studied and found that some of them represent gravitational collapse of an anisotropic fluid.

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