A critical dimension for the stability of perfect fluid spheres of radiation
arXiv:0707.0961 · doi:10.1088/0264-9381/25/20/205010
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.
18 pages, 5 figures; v2 reference and footnote added; v3 slight reordering of content, new section added with further analysis; v4 Final version - small changes, including a new title, accepted for publication in CQG