Critical behavior and scaling in vacuum axisymmetric gravitational collapse

Abstract

We report a second example of critical behavior in gravitational collapse. Collapse of axisymmetric gravitational wave packets is computed numerically for a one-parameter family of initial data. A black hole first appears along the sequence at a critical parameter value ${\mathit{p}}^{\mathrm{*}}$. As with spherical scalar-field collapse, a power law is found to relate black-hole mass (the order parameter) and critical separation: ${\mathit{M}}_{\mathrm{BH}}$\ensuremath{\propto}\ensuremath{\Vert}p-${\mathit{p}}^{\mathrm{*}}$${\mathrm{\ensuremath{\Vert}}}^{\mathrm{\ensuremath{\beta}}}$. The critical exponent is \ensuremath{\beta}\ensuremath{\simeq}0.37, remarkably close to that observed by Choptuik. Near-critical evolutions produce echoes from the strong-field region which appear to exhibit scaling.