Regular and conformal regular cores for static and rotating solutions

Using a new metric for generating rotating solutions, we derive in a general fashion the solution of an imperfect fluid and that of its conformal homolog. We discuss the conditions that the stress-energy tensors and invariant scalars be regular. On classical physical grounds, it is stressed that, conformal fluids used as cores for static or rotating solutions, are exempt from any malicious behavior in that they are finite and defined everywhere.