Varieties of Parametric Classes of Exact Solutions in General Relativity Representing Static Fluid Balls

Neeraj Pant

doi:10.5402/2011/749396

Abstract

We have presented a method of obtaining parametric classes of spherically symmetric analytic solutions of the general relativistic field equations in canonical coordinates. A number of previously known classes of solutions have been rediscovered which describe perfect fluid balls with infinite central pressure and infinite central density though their ratio is positively finite and less than one. From the solution of one of the newly discovered classes, we have constructed a causal model in which outmarch of pressure and density is positive and monotonically decreasing, and pressure-density ratio is positive and less than one throughout within the balls. Corresponding to this model, we have maximized the Neutron star mass 2.40MΘ with the linear dimensions of 28.43 kms and surface red shift of 0.4142.

Highlights

Due to nonlinearity of the Einstein’s field equations, many attempts have been reported to obtain parametric classes of exact solutions of representing perfect fluid ball in equilibrium such as Tolman [1], Wyman [2], Kuchowich [3], Pant and Sah [4], D.N
In addition to the parameter l, the solutions (??) contain three arbitrary constants C1, C2, and A. These are to be determined by matching the solutions (??) with Schwarzschild exterior solution for a ball of mass M and linear dimension 2rb: p(rb) = 0, e−λ(rb) = 1 − 2u, (25)
We present here a model of Neutron star based on the particular solution discussed above

Summary

Introduction

Due to nonlinearity of the Einstein’s field equations, many attempts have been reported to obtain parametric classes of exact solutions of representing perfect fluid ball in equilibrium such as Tolman [1], Wyman [2], Kuchowich [3], Pant and Sah [4], D.N. Pant [5], Pant [6, 7], Pant [8], Delgaty, Lake [9], Lake [10], Tewari and Pant [11], and Maurya, Gupta [12]. The usual boundary conditions determine three arbitrary constants leaving one undetermined; such a solution represents a class of solutions, with undetermined constant being a parameter. In the light of importance of parametric class, in this paper, we present a variety of parametric classes of solutions

Field Equations and Method of Obtaining Parametric Classes of Solutions

Varieties of Classes of Solutions

Properties of the New Class of Solutions

Some More Parametric Classes of Solutions

Conclusion