Choptuik’s scaling in higher dimensions

Abstract

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 $4\ensuremath{\le}D\ensuremath{\le}11$ 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 $\ensuremath{\gamma}$ and the echoing period $\ensuremath{\Delta}$. The behavior of these numbers with increasing dimension seems to indicate that $\ensuremath{\gamma}$ reaches a maximum and $\ensuremath{\Delta}$ a minimum value around $11\ensuremath{\le}D\ensuremath{\le}13$. These results and their relation to the black hole--black string system are discussed.