Simulating Black Hole Collapse from Axisymmetric Scalar Fields using Modern Finite Difference Techniques

In the parameter space near the threshold of black hole formation (given arbitrary initial data) numerical analysis reveals an intriguing degree of structure to resulting spacetimes, namely power-law mass scaling, universality, and self-similarity. These solutions have proven to be a powerful test of cosmic censorship, as well as provide a potential physical mechanism for the formation of primordial black holes. However, while this "critical phenomena" is well replicated in the spherically symmetric case, there has been much less success in higher dimensional spaces, particularly when it comes to universality and self-similarity. Currently, research on critical phenomena is mostly focused on investigating fully three-dimensional spacetimes, which severely limits both computational speed and achievable accuracy. To address this, we implement and apply modern advances in the finite difference method (FDM) to the problem of the axisymmetric critical collapse of scalar fields. This provides a model system for investigating the coupling of matter and the gravitational field in critical collapse, while also enabling significant accuracy improvements. We present initial results in studying critical collapse using our FDM mixed elliptic-hyperbolic code.