Shear-free perfect fluids in general relativity. I. Petrov type N Weyl tensor

Abstract

Petrov type N, shear-free, perfect fluid solutions of the Einstein field equations are investigated. It is shown that if the fluid pressure p and energy density w are related by a barotropic equation of state p=p(w) satisfying w+p≢0, and if the Weyl tensor is of Petrov type N then the fluid’s volume expansion is zero but the vorticity is necessarily nonzero. The differential equation determining p as a function of w is given. For this class of solutions the fluid’s vorticity vector is orthogonal to the acceleration.