A critical dimension for the stability of perfect fluid spheres of radiation

TL;DR

This paper investigates the stability of radiating perfect fluid spheres in asymptotically AdS spacetimes, identifying a critical dimension (eleven) where the behavior changes from oscillatory to monotonic mass increase.

Contribution

It introduces the concept of a critical dimension affecting the stability of perfect fluid stars in AdS, highlighting a transition at eleven dimensions.

Findings

Mass increases monotonically in high dimensions

Oscillations in mass appear in lower dimensions

Critical dimension for stability is eleven

Abstract

An analysis of radiating perfect fluid models with asymptotically AdS boundary conditions is presented. Such scenarios consist of a spherical gas of radiation (a "star") localised near the centre of the spacetime due to the confining nature of the AdS potential. We consider the variation of the total mass of the star as a function of the central density, and observe that for large enough dimensionality, the mass increases monotonically with the density. However in the lower dimensional cases, oscillations appear, indicating that the perfect fluid model of the star is becoming unrealistic. We find the critical dimension separating these two regimes to be eleven.