arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2007.12164gr-qc
收藏

$2+1$维中刚性旋转的理想流体星

Rigidly rotating perfect fluid stars in $2+1$ dimensions

Carsten Gundlach, Patrick Bourg

备注：
Added references. This version accepted by PRD
发表信息：
Phys. Rev. D 102, 084023 (2020)
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

Cataldo已经发现了2+1维中所有刚性旋转的自引力完美流体解，其宇宙常数为负$Λ$，密度先验地指定为某个径向坐标的函数。对于任意正压状态方程$p(ρ)$，我们在标准极径坐标下改写了这些解。对于任何给定的状态方程，我们发现的两个参数家庭的解决方案与一个经常的中心和有限的总质量$M$和角动量$J$（刚性旋转的恒星）。对于解析状态方程，其解除了在表面是解析的，但包括在中心。定义无量纲自旋$\tilde J:=\sqrt{-Λ}\,J$，对于区域$|\tilde J|-1<M<|\tilde J|$中的每个$(\tilde J,M)$，精确地存在一个解，该区域由点粒子区域$M<-|\tilde J|$和过自旋区域$|\tilde J|>|M|$的部分组成。在黑洞区域$|\tilde J|<M$（其范围取决于状态方程）的相邻紧凑部分中，每个$(\tilde J,M)$精确地有两个解。因此，外解存在于所有三类BTZ解（黑洞、点粒子和超旋）中，但并非所有可能的$(\tilde J,M)$值都可以实现为恒星。不管$\tilde J$和$M$的值如何，所有状态方程的所有恒星的因果结构都是反德西特空间的因果结构，没有视界或封闭的类时曲线。

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

↑