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

TL;DR

This paper constructs a class of smooth, rotating spacetime models with de Sitter cores and Kerr exteriors, potentially representing gravastars or black hole mimickers, and discusses their geometric and energy condition properties.

Contribution

It introduces a method for creating arbitrarily differentiable transitions between de Sitter interiors and Kerr exteriors in Einstein gravity, expanding the modeling of black hole mimickers.

Findings

Models can have a smooth $C^{n}$ transition from de Sitter to Kerr.

Energy conditions can be satisfied in the outer layers of the transition.

Topological change in the ergosphere from $S^{2}$ to $S^{1} imes S^{1}$ occurs.

Abstract

Within the paradigm of non-perturbative Einstein gravity we study continuous curvature 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 $C^{n}$ metric 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.