Slowly rotating dust sphere for free space in general relativity with uniform matter distribution

Abstract

Einstein field equations for a charged dusty universe have already investigated. In this paper we present a new class of analytical solutions in terms of canonical coordinates for Einstein’s field equations; assuming that the spacetime is spherically symmetric, formed by non-charged dust with uniform matter distribution. The metric we considered is of the form, ds2 = e2ndt2 −e2ldr2−r2dq2−r2 sin2 q(df − Wdt)2, where n,l and W are functions of the radial coordinate r only. Our model has only a space singularity at r =0 and the solutions are well behaved for r > 0. In addition, we assume that the proper density r is constant. W(r), the angular velocity of the inertial frame; can be an arbitrary function of r, which satisfies required boundary conditions to be a slow rotation.