  Within the paradigm of non-perturbative Einstein gravity we study continuous
manifolds which possess de Sitter interiors and Kerr exteriors. These manifolds
could represent the spacetime of rotating gravastars or other similar black
hole mimickers. The scheme presented here allows for a $C^{n}$ transition from
the exactly de Sitter interior to the exactly Kerr exterior, with $n$
arbitrarily large. Generic properties that such models must possess are
discussed, such as the changing of the topology of the ergosphere from $S^{2}$
to $S^{1}\times S^{1}$. It is shown how in the outer layers of the transition
region (the "atmosphere" as it is often called in astrophysics) the
dominant/weak and strong energy conditions can be respected. However, much like
in the case of its static spherically symmetric gravastar counterpart, there
must be some assumptions imposed in the atmosphere for the energy conditions to
hold. These assumptions turn out to not be severe. The class of manifolds
presented here are expected to possess all the salient features of the fully
generic case. Strictly speaking, a number of the results are also applicable to
the locally anti-de Sitter core scenario, although we focus on the case of a
positive cosmological constant.
