Evaluating 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 in homogeneous 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 explicit y shown that the considered matter is non-exotic, that is, it does not violate the energy conditions. Also, static solutions are studied. Tere is only one static solution: a conical spacetime