论文标题
严格旋转完美的流体星，$ 2+1 $尺寸
Rigidly rotating perfect fluid stars in $2+1$ dimensions
论文作者
论文摘要
Cataldo发现在2+1个尺寸中，所有刚性旋转的自我修饰的完美流体溶液，具有负宇宙常数$λ$，因为密度为先验的密度是特定径向坐标的函数。我们将这些解决方案重写为标准的极性坐标，用于状态$ p（ρ）$的任意正压方程。对于任何给定的状态方程式，我们发现具有常规中心和有限的总质量$ m $和Angular Momentum $ J $（严格旋转的星星）的两参数解决方案家族。对于状态的分析方程，该解决方案是分析性的，除了表面，但包括中心。定义无量纲的自旋$ \ tilde J：= \ sqrt {-λ} \，j $，在区域中，每个$（\ tilde j，m）$ cy $ | \ tilde j | -1 <m <m <| \ tilde j | $ cys $ | \ tilde j | -1 <m <| \ tilde j | $ | \ tilde J |> | m | $。在黑洞区域的相邻紧凑部分$ | \ tilde j | <m $（其范围取决于状态方程），每个$（\ tilde j，m）$恰好有两个解决方案。因此，在所有三类BTZ溶液（黑洞，点粒子和超螺旋）中，外部解决方案都存在，但并非所有可能的$（\ tilde j，m）$的所有可能值都可以用作恒星。无论$ \ tilde j $和$ m $的值如何，所有状态方程的全明星的因果结构都是反de保姆空间，没有水平或封闭的时间表曲线。
Cataldo has found all rigidly rotating self-gravitating perfect fluid solutions in 2+1 dimensions with a negative cosmological constant $Λ$, 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 $p(ρ)$. 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 $\tilde J:=\sqrt{-Λ}\,J$, there is precisely one solution for each $(\tilde J,M)$ in the region $|\tilde J|-1<M<|\tilde J|$, which consists of parts of the point particle region $M<-|\tilde J|$ and overspinning regions $|\tilde J|>|M|$. In an adjacent compact part of the black hole region $|\tilde J|<M$ (whose extent depends on the equation of state), there are precisely two solutions for each $(\tilde J,M)$. Hence exterior solutions exist in all three classes of BTZ solution (black hole, point particle and overspinning), but not all possible values of $(\tilde J,M)$ can be realised as stars. Regardless of the values of $\tilde J$ and $M$, the causal structure of all stars for all equations of state is that of anti-de Sitter space, without horizons or closed timelike curves.
