Critical Dimension for Stable Self-gravitating Stars in AdS

TL;DR

This paper investigates the stability of self-gravitating stars in Anti-de Sitter space with a linear equation of state, identifying a critical dimension that determines their stability properties.

Contribution

It introduces the concept of a critical dimension for stability of stars in AdS space, depending on the equation of state parameter, and clarifies the minimum stable dimension.

Findings

Critical dimension depends on the parameter a

Stars are stable above a certain dimension regardless of central density

Lowest stable dimension is 12 for all a in [0,1]

Abstract

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.