On Choptuik's scaling in higher dimensions

We extend Choptuik's scaling phenomenon found in general relativistic critical gravitational collapse of a massless scalar field to higher dimensions. We find that in the range $4 \leq D \leq11$ the behavior is qualitatively similar to that discovered by Choptuik. In each dimension we obtain numerically the universal numbers associated with the critical collapse: the scaling exponent $\gamma$ and the echoing period $\Delta$. The behavior of these numbers with increasing dimension indicates the existence of a {\it critical dimension} around $11 \leq D \leq 13$ where $\gamma$ reaches a maximum and $\Delta$ a minimum value. These results and their relation to the black hole--black string system are discussed