标题： 关于一类精确的任意可微的德西特核心与克尔外部结构：可能的真空星或常规黑洞模仿者 显示英文标题

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

摘要： 在非微扰爱因斯坦引力的框架下，我们研究具有德西特内部和克尔外部的连续曲率流形。 这些流形可能代表旋转的真空星或其它类似的黑洞替代物的时空。 这里提出的方案允许从精确的德西特内部到精确的克尔外部的$C^{n}$度规过渡，其中$n$可以任意大。 讨论了这类模型必须具备的一些通用特性，例如能层的拓扑从$S^{2}$到$S^{1}\times S^{1}$的变化。 展示了在外层过渡区域（通常在天体物理学中称为“大气层”）中，主能量条件和弱能量条件以及强能量条件可以得到满足。 然而，与静态球对称真空星的情况类似，为了使能量条件成立，必须在大气层中施加一些假设。 这些假设被证明并不严重。 这里提出的流形类预计会具备完全一般情况下的所有显著特征。 严格来说，一些结果也适用于局部反德西特核心情景，尽管我们专注于正宇宙常数的情况。 显示英文摘要

摘要： 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.