scholarly journals Spherically Symmetric Charged Dust Distribution in General Relativity. I. General Solution

1980 ◽  
Vol 33 (4) ◽  
pp. 765 ◽  
Author(s):  
BK Nayak
Keyword(s):  
General Relativity ◽  
General Solution ◽  
Charge Density ◽  
Mass Density ◽  
Maxwell Field ◽  
Charged Dust ◽  
Spherically Symmetric ◽  
Field Equations ◽  
Mathematical Condition ◽  
Dust Distribution

The Einstein-Maxwell field equations characterizing a spherically symmetric charged dust distnbution are solved exactly without imposing any mathematical condition on them. The solution is expressed in terms of two arbitrary variables and these can be chosen to correspond to an arbitrary ratio of charge density to mass density, thus allowing the possibility of understanding the interior of the horizon in a more precise manner.

Cylindrically symmetric charged dust distributions in rigid rotation in general relativity

1968 ◽  
Vol 304 (1476) ◽  
pp. 81-86 ◽  
Keyword(s):  
General Relativity ◽  
Charge Density ◽  
Lorentz Force ◽  
Maxwell Equations ◽  
Mass Density ◽  
Rigid Rotation ◽  
Charged Dust ◽  
Cylindrically Symmetric ◽  
Classical Analogue ◽  
Dust Distribution

The paper presents a family of stationary cylindrically symmetric solutions of the Einstein-Maxwell equations corresponding to a charged dust distribution in rigid rotation. The interesting feature of the solution is that the Lorentz force vanishes everywhere and the ratio of the charge density and mass density may assume arbitrary value. The solutions do not seem to have any classical analogue.

scholarly journals Nonstatic Spherically Symmetric Isotropic Solutions for a Perfect Fluid in General Relativity

1978 ◽  
Vol 31 (1) ◽  
pp. 111 ◽  
Author(s):  
Max Wyman
Keyword(s):  
Differential Equation ◽  
General Relativity ◽  
General Solution ◽  
Present Author ◽  
Spherically Symmetric ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Perfect Fluids ◽  
Specific Choice ◽  
Total Differential

The present author (Wyman 1946) showed that all perfect fluids which can be represented by nonstatic, spherically symmetric, isotropic solutions of the Einstein field equations can be found by solving a nonlinear total differential equation of the second order involving. an arbitrary function 'P(r). Since then several particular solutions of this equation have been found. Although the four solutions given recently by Chakravarty et at. (1976) involve particular choices of 'P(r), none of these is the general solution of the equation that results from the specific choice of 'P(r) that was made. The present paper shows how these four general solutions are obtained.

Static distribution of charged dust in general relativity

1968 ◽  
Vol 303 (1472) ◽  
pp. 97-101 ◽  
Keyword(s):  
General Relativity ◽  
Charge Density ◽  
Poisson Equation ◽  
Electrostatic Potential ◽  
Empty Space ◽  
Simple Relation ◽  
Matter Density ◽  
Charged Dust ◽  
Field Equations ◽  
Equipotential Surfaces

The paper considers charged dust distributions in equilibrium. If the dust be uniformly charged (i. e. if the ratio of the charge density to the matter density be constant) or if the surfaces of the dust distributions be equipotential surfaces and inside these surfaces there is no hole or pocket of alien matter, then there exists a simple relation between and g 00 and ϕ , the electrostatic potential and the charge density must be equal to the matter density. Further in this case, the whole system of field equations can be reduced to a single Laplace equation in the empty space outside and to a nonlinear modified Poisson equation within the charged dust distributions.

scholarly journals Static Charged Dust Distribution in the Brans-Dicke Theory

1975 ◽  
Vol 28 (5) ◽  
pp. 585 ◽  
Author(s):  
BK Nayak
Keyword(s):  
Charge Density ◽  
Mass Density ◽  
Charged Dust ◽  
Scalar Interaction ◽  
Theory Of Gravitation ◽  
Dust Distribution

The distribution of static charged dust in the Brans-Dicke theory is considered. It is shown that the ratio of charge density to mass density is related to the scalar interaction '" so that for small values of '" the charge density will far exceed the mass density. This result suggests that the existence of a finite electron can be realized in the Brans-Dicke theory of gravitation through a static charged dust distribution.

Approximate solutions of the general relativity field equations with a scalar meson field

1963 ◽  
Vol 59 (4) ◽  
pp. 739-741 ◽  
Author(s):  
J. Hyde
Keyword(s):  
General Relativity ◽  
Scalar Meson ◽  
Empty Space ◽  
Approximate Solutions ◽  
Spherically Symmetric ◽  
Coordinate Transformations ◽  
Field Equations ◽  
Spherically Symmetric Solution ◽  
Image Position ◽  
Scalar Meson Field

It was shown by Birkhoff ((1), p. 253) that every spherically symmetric solution of the field equations of general relativity for empty space,may be reduced, by suitable coordinate transformations, to the static Schwarzschild form:where m is a constant. This result is known as Birkhoff's theorem and excludes the possibility of spherically symmetric gravitational radiation. Different proofs of the theorem have been given by Eiesland(2), Tolman(3), and Bonnor ((4), p. 167).

Exact solution of a static charged sphere in general relativity

1969 ◽  
Vol 47 (21) ◽  
pp. 2401-2404 ◽  
Author(s):  
S. J. Wilson
Keyword(s):  
Exact Solution ◽  
General Relativity ◽  
Gravitational Constant ◽  
The Self ◽  
Spherically Symmetric ◽  
Charged Sphere ◽  
Field Equations ◽  
First Order ◽  
Self Energy ◽  
Spherically Symmetric Distribution

An exact solution of the field equations of general relativity is obtained for a static, spherically symmetric distribution of charge and mass which can be matched with the Reissner–Nordström metric at the boundary. The self-energy contributions to the total gravitational mass are computed retaining only the first order terms in the gravitational constant.

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