Invariant solutions of Einstein field equation for nonconformally flat fluid spheres of embedding class one

Abstract

In the present paper, nonconformal spherical symmetric perfect fluid solutions to Einstein field equations are obtained by using the invariance of the equations under the Lie group of transformations and some new solutions of this category are obtained satisfying the reality conditions like Ï â‰¥ p ≥ 0, Ï r < 0, pr < 0 (p and Ï being pressure and energy-density respectively) in the region 0 < r < a. Such fluids do not represent isolated fluid spheres as pressure free interface is not possible for nonconformally perfect fluids of class one. © 2010 World Scientific Publishing Company.