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 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.

scholarly journals On Stationary Distributions of Charged Dust

1976 ◽  
Vol 29 (2) ◽  
pp. 119 ◽  
Author(s):  
A Banerjee ◽  
N Chakravarty ◽  
SB Dutta Choudhury
Keyword(s):  
Charge Density ◽  
Lorentz Force ◽  
Stationary Distribution ◽  
Arbitrary Constant ◽  
Mass Density ◽  
Charged Dust ◽  
Stationary Distributions ◽  
Incorrect Result

The correct value of the ratio of charge density to mass density is obtained for a stationary distribution of charged dust with vanishing Lorentz force. It is found that the ratio is truly an arbitrary constant, in disagreement with the apparently. incorrect result obtained by Misra et al. (1972).

On rotating charged dust in general relativity. V

1983 ◽  
Vol 389 (1797) ◽  
pp. 291-298 ◽  
Keyword(s):  
General Relativity ◽  
Maxwell Equations ◽  
Interior Solution ◽  
Charged Dust ◽  
Exterior Solution ◽  
Cylindrically Symmetric

We find an exact cylindrically symmetric stationary exterior solution of the Einstein-Maxwell equations. We then match this solution smoothly onto an interior solution for rotating charged dust found earlier by the author. The solution thus obtained is regular and well behaved inside the matter. Such matched solutions are rare either for the Einstein or Einstein-Maxwell equations. Some properties of the solution are discussed.

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.

On rotating charged dust in general relativity. III

1980 ◽  
Vol 372 (1748) ◽  
pp. 111-115 ◽  
Keyword(s):  
General Relativity ◽  
Maxwell Equations ◽  
Arbitrary Constant ◽  
Interesting Property ◽  
Interior Solution ◽  
Charged Dust ◽  
Constant Ratio ◽  
Cylindrically Symmetric

An earlier paper considered an exact cylindrically symmetric interior solution of the Einstein-Maxwell equations for rotating charged dust corresponding to a definite constant ratio of the charge and mass of the particles. In this paper a new, exact cylindrically symmetric interior solution is found which corresponds to an arbitrary constant ratio of the charge and mass. An interesting property of the new solution is that it is regular and well behaved for certain values of the parameters occurring in it.

On rotating charged dust in general relativity

1978 ◽  
Vol 362 (1710) ◽  
pp. 329-340 ◽  
Keyword(s):  
General Relativity ◽  
Exact Solutions ◽  
Differential Rotation ◽  
Single Equation ◽  
Charged Dust ◽  
Newtonian Physics ◽  
Coupled Equations ◽  
Cylindrically Symmetric ◽  
Axis Of Symmetry

The problem of charged dust rotating about an axis of symmetry is considered both in Newtonian physics and in general relativity. The Newtonian problem is reduced to a single equation in the case of constant rotation, and to two coupled equations in the case of differential rotation, and some explicit cylindrically symmetric solutions are obtained. In general relativity some new cylindrically symmetric exact solutions for constant rotation are derived, and the problem of differential rotation is reduced to four coupled equations for four unknowns.

scholarly journals CYLINDRICALLY SYMMETRIC SPINNING BRANS–DICKE SPACE–TIMES WITH CLOSED TIMELIKE CURVES

1999 ◽  
Vol 14 (17) ◽  
pp. 1105-1111 ◽  
Author(s):  
LUIS A. ANCHORDOQUI ◽  
SANTIAGO E. PEREZ BERGLIAFFA ◽  
MARTA L. TROBO ◽  
GRACIELA S. BIRMAN
Keyword(s):  
General Relativity ◽  
Exact Solutions ◽  
Cylindrical Symmetry ◽  
Space Time ◽  
Rigid Rotation ◽  
Closed Timelike Curves ◽  
New Exact Solutions ◽  
Cylindrically Symmetric

We present here three new exact solutions of Brans–Dicke theory for a stationary geometry with cylindrical symmetry in the presence of matter in rigid rotation with [Formula: see text]. All the solutions have eternal closed timelike curves in some region of space–time which has a size that depends on ω. Moreover, two of them do not go over a solution of general relativity in the limit ω→∞.

Rotating charged dust as a source for cylindrically symmetric electrovacs

1984 ◽  
Vol 394 (1807) ◽  
pp. 437-447 ◽  
Keyword(s):  
Electromagnetic Field ◽  
General Solution ◽  
Exact Solutions ◽  
Cylindrical Symmetry ◽  
Rigid Rotation ◽  
Charged Dust ◽  
Mass Ratio ◽  
Cylindrically Symmetric ◽  
Free Electromagnetic Field ◽  
Constant Charge

Exact solutions for stationary rotating charged dust with cylindrical symmetry, for which one of the spacelike Killing vectors is hypersurface orthogonal, are considered. The general solution for the case of rigid rotation and constant charge to mass ratio is given. It is proved that all rigidly rotating solutions can be joined smoothly to the exterior electrovac solutions involving third Painlevé transcendents. Also the solutions for differentially rotating charged dust, which have a force-free electromagnetic field can be matched to a particular class of the electrovac metrics.

On rotating charged dust in general relativity. IV

1983 ◽  
Vol 385 (1788) ◽  
pp. 189-205 ◽  
Keyword(s):  
General Relativity ◽  
Angular Velocity ◽  
Interesting Property ◽  
Equal Mass ◽  
Constant Angular Velocity ◽  
Charged Dust ◽  
Axially Symmetric ◽  
Maxwell Theory ◽  
Cylindrically Symmetric ◽  
Main Equation

In this paper we derive four main results. Firstly, we find an exact and explicit non-cylindrically symmetric (but axially symmetric) solution for charged dust rotating with constant angular velocity in Newton-Maxwell theory for particles with equal mass and charge. Secondly, we find a general solution of the main equation describing differential rotation in Newton-Maxwell theory for particles of equal mass and charge. Thirdly, we derive a new exact and explicit solution of the cylindrically symmetric Einstein-Maxwell interior equations for charged dust rotating with constant angular velocity. An interesting property of the solution is that it is regular and well behaved for certain values of the parameters occurring in it. Fourthly, we show that for cylindrically symmetric, differentially rotating charged dust in general relativity there exists a solution in which the Lorentz force on a typical particle vanishes.

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