Some Charged Fluid Spheres in General Relativity

Solutions and Conditions for Charged Fluid Spheres in General Relativity

by Mukesh Kumar Madhukar*,

- Published in Journal of Advances and Scholarly Researches in Allied Education, E-ISSN: 2230-7540

Volume 17, Issue No. 1, Apr 2020, Pages 606 - 608 (3)

Published by: Ignited Minds Journals


ABSTRACT

The present paper provides some solutions of Einstein Maxwell field equations for Some Charged Fluid Spheres by using a judicious choice of metric potential g11 and g44. The central and boundary conditions have been also discussed

KEYWORD

charged fluid spheres, general relativity, Einstein Maxwell field equations, metric potential, central and boundary conditions

INTRODUCTION

A various authors have already studied the charged fluid distribution in equilibrium. Bonner [4], Effinger [6] and Kyle and Martin [11] have considered the interior solution for a static charged sphere. As the field equations do not completely determine the system different solutions were obtained by Effinger [6], Wilson [16) and Kyle and Martin [11] by using different conditions. Some exact static solutions of Einstein-Maxwell equations representing a charged fluid sphere were obtained by Singh and Yadav [14]. Shi-Chang [15] found some conformal flat interior solutions of the Einstein-Maxwell equations for a charged stable static sphere. These solutions satisfy physical conditions inside the sphere. Xingxiang [18] obtained an exact solution by specifying matter distribution and charge distribution. The metric is regular and can be matched to the Reissner-Nordstrom metric and pressure is finite. In the limit of vanishing charge, the solution reduces to the interior solution of an uncharged sphere. Buchdahl [5] has also considered some regular general relativistic charged fluid spheres. Some other cases of the interior solutions for charged fluid sphere have been presented by Bekenstein[3], Bailyn[2], Whiman and Burch [17], Kramer and Neugebauer [9], Krori and Barua [10], Junevicous[8], Florides [7], Noluka[12, 13] and Yadav et. al. [19, 20]. Some other researchers in this field are Pradhan [21], Yilmaz (22) and Saha & Visinescu [23]. In this paper, we have solved Einstein-Maxwell field equations for static changed fluid spheres by using different assumptions. These solutions satisfy physical conditions. The central and boundary conditions have been also discussed. The pressure and density have been found for the distribution.

THE FIELD EQUATIONS

We take the metric in the form where and v are function of r only. Thus the Einstein-Maxwell field equations are (Adler et. al. [1]]. where and By the use of equations (2.2) – (2.4), we get the expressions for p,  and E as

SOLUTION OF THE FIELD EQUATIONS

We have four equations (2.2) – (2.4) and (2.6) in six variables(,E,p,,,). Hence the two variables are free. We take u and v as the two free variables. Here we choose. and where a1, a2, c, d, g and k are constant and n positive integer (n0). Then equations (2.6) . (2.9) yield Now matching the solution with Reissner-Nordstron metric at the boundary r = r0, we have In particular, if we take a1 = g = 0, then we get and At r = 0, these result give and For p0 and 0 to be positive we must have Further for 003p From conditions (3.17) and (3.18), we have Again matching the solution with Reissner-Nordstrom metric at boundary r = rb, we get and

REFERENCES

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Corresponding Author Mukesh Kumar Madhukar*

Associate Professor, Dept. of Mathematics, M. M. College, Bikram, Patna, Patliputra University, Patna