Dimension-Dependence of the Critical Exponent in Spherically Symmetric Gravitational Collapse

Abstract

We study the critical behaviour of spherically symmetric scalar field collapse to black holes in spacetime dimensions other than four. We obtain reliable values for the scaling exponent in the supercritical region for dimensions in the range $3.5\\leq D\\leq 14$. The critical exponent increases monotonically to an asymptotic value at large $D$ of $\\gamma\\sim0.465$. It is fairly well fit by the simple relationship: $\\gamma=0.465(1-e^{-0.412D})$.