标题： 稳定自引力恒星在AdS中的临界维度 显示英文标题

标题： Critical Dimension for Stable Self-gravitating Stars in AdS

摘要： 我们研究了在AdS空间中具有线性状态方程$P=a \rho$的自引力恒星，其中$a$是一个常数参数。 存在一个临界维度，超过该维度后，恒星在任何中心能量密度下都是稳定的；低于该维度时，对于一定的中心能量密度存在最大质量配置，当中心能量密度继续增加时，该配置变得不稳定。 我们发现临界维度取决于参数$a$，它随着$a$从$a=0$变化到1而从$d=11.1429$变化到10.1291。 动态稳定自引力结构的最低整数维度应为$d=12$对于任何$a \in [0,1]$而不是$d=11$，后者是AdS空间中自引力辐射结构的情况。 显示英文摘要

摘要： We study the self-gravitating stars with a linear equation of state, $P=a \rho$, in AdS space, where $a$ is a constant parameter. There exists a critical dimension, beyond which the stars are always stable with any central energy density; below which there exists a maximal mass configuration for a certain central energy density and when the central energy density continues to increase, the configuration becomes unstable. We find that the critical dimension depends on the parameter $a$, it runs from $d=11.1429$ to 10.1291 as $a$ varies from $a=0$ to 1. The lowest integer dimension for a dynamically stable self-gravitating configuration should be $d=12$ for any $a \in [0,1]$ rather than $d=11$, the latter is the case of self-gravitating radiation configurations in AdS space.