On a Class of Exact Arbitrarily Differentiable de Sitter Cores with Kerr Exteriors: Possible gravastar or regular black hole mimickers

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.