Cataldo has found all rigidly rotating self-gravitating perfect fluid solutions in 2+1 dimensions with a negative cosmological constant $\Lambda$, for a density that is specified a priori as a function of a certain radial coordinate. We rewrite these solutions in standard polar-radial coordinates, for an arbitrary barotropic equation of state $p(\rho )$. For any given equation of state, we find the two-parameter family of solutions with a regular centre and finite total mass $M$ and angular momentum $J$ (rigidly rotating stars). For analytic equations of state, the solution is analytic except at the surface, but including at the centre. Defining the dimensionless spin $\tilde{J}:=\sqrt{-\Lambda }J$, there is precisely one solution for each $(\tilde{J},M)$ in the region $|\tilde{J}|-1|M|$. In an adjacent compact part of the black hole region $|J|

中文翻译：

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以2 + 1维刚性旋转完美的流体恒星

Cataldo已发现所有2 + 1维具有负宇宙学常数的刚性旋转自重完美流体解决方案 $\Lambda$，对于根据先验确定的密度作为某个径向坐标的函数。对于标准的任意正压状态方程，我们将这些解重写为标准的极坐标系$p（\rho ）$。对于任何给定的状态方程，我们找到具有规则中心和有限总质量的两参数解系列$\mathrm{中号}$ 和角动量 $Ĵ$（刚性旋转的星星）。对于状态解析方程，除了在表面但包括在中心之外，解决方案都是解析的。定义无量纲旋转$\widetilde{Ĵ}：=\sqrt{-\Lambda }Ĵ$，每种方法都有一个解决方案 $（\widetilde{Ĵ}，\mathrm{中号}）$ 在该区域 $|\widetilde{Ĵ}|-\mathrm{1个}|\mathrm{中号}|$。在黑洞区域的相邻紧致部分$ | J |