Inhomogeneous cosmologies: New exact solutions and their evolution

Abstract

An algorithm is presented for determining all solutions of the Einstein field equations representing a perfect fluid with metric of the form ds2=dt2−e2αdz2 −e2β(dx2+dy2) and fluid flow vector u=∂/∂t. The entire class of solutions is then invariantly characterized. These new solutions generalize Szekeres’ inhomogeneous cosmological models containing dust. A subclass of these solutions is studied in detail and it is interesting that some of these models approach isotropy but not homogeneity for large cosmological times.