Evolving spacetimes with purely radial tension

In this study time-dependent and spherically symmetric solutions of the Einstein field equations in an anisotropic background with a purely radial tension are presented. There exist three classes of solutions,1) An open spacetime with a wormhole at its center. 2) A conical spacetime. 3) A closed spacetime. These inhomogeneous solutions are reduced to FRW spacetimes in matter-dominated era, asymptotically. Therefore, they can be used to describe local inhomogeneities that are not considered in the standard model. For the wormhole solution. it is explicity shown that the considered matter is non-exotic, that is, it does not violate the energy conditions. Also, static solutions are studied. There is only one static solution,a conical spacetime. In this case, the matter satisfies the energy condition critically.