Critical Phenomena in Non-spherically Symmetric Scalar Bubble Collapse

Abstract: We investigate numerically the critical behaviour which occurs in the collapse of both spherically symmetric and asymmetric scalar field bubbles with full general relativity. We use a minimally coupled scalar field subject to a "double well" interaction potential, with the bubble wall spanning the barrier between two degenerate minima. We find that the spherically symmetric case exhibits Type 2 critical behaviour with the critical index consistent with a value of gamma = 0.37 as expected. In the asymmetric case, we find that again our results are consistent with a value of gamma = 0.37 for the dominant unstable mode. We do not see strong evidence of echoing in the solutions, which could be due to the fact that the coordinates are not well adapted to the echoing behaviour, or due to being still too far from the critical point to properly observe the critical solution.