Presentation description

The critical formation of black holes, as first discovered by Matthew Choptuik, yields a surprising amount of structure and generality. Giving rise to power-law scaling of mass, echoing behavior, and (violating cosmic censorship) naked curvature singularities. However, while such ""critical phenomena"" have been extensively studied and understood in spherically symmetry, it has been markedly harder to obtain such results in less symmetric spacetimes with a reasonable accuracy. Specifically, in a followup work Choptuik discovered an intriguing phenomena in axisymmetric scalar field collapse, where the critical solution would bifurcate into two echoing solutions. But (due to computational constraints) he was neither able to verify the universality of this phenomena, nor whether such solutions are self-similar. To address this, we build a code utilizing more recent advancements in numerical analysis to simulate axisymmetric spacetimes, including the High Order Finite Difference Method (HOFDM) and block-structured Adaptive Mesh Refinement (AMR). Here we present our preliminary implementation of this method and our analysis of solutions for axisymmetric scalar field initial data.