Fluid sphere: Stability problem and dimensional constraint

Abstract

We study different dimensional fluids inspired by noncommutative geometry which admit conformal Killing vector (CKV). The solutions of the Einstein field equations were examined specifically for five different set of spacetime. We calculate the active gravitational mass and impose stability conditions of the fluid sphere. The analysis thus carried out immediately indicates that at four dimension only one can get a stable configuration for any spherically symmetric stellar system and any other dimension, lower or higher, becomes untenable as far as the stability of a system is concerned.