Higher dimensional Choptuik scaling in Painleve-Gullstrand coordinates

We investigate Choptuik scaling in the spherically symmetric collapse of a massless scalar field in higher dimensions using Painleve-Gullstrand coordinates. Our analysis gives reliable results for the critical exponent and period echoing up to seven dimensions and confirms the presence in higher dimensions of the cusps in the periodic scaling relationship recently observed in four dimensional collapse. In addition, our value for the critical exponent in seven dimensions is consistent with that obtained by Bland et al., who argued that the critical exponent increases monotonically with dimension to an asymptotic value of $1/2$.

Figure 1

Mass Scaling in four, five, six, and seven dimensions with the $A$ parameter varied.

Figure 2

Mass Scaling in eight dimensions ($A$ varied).