Research

Einstein's equations are a set of coupled, nonlinear partial differential equations, and as a result of their complexity, solutions may oftentimes only be found by numerical techniques. The problem of finding these solutions for astrophysically relevant situations is the essence of Numerical Relativity. We detail here a few of the facets of this ongoing effort, and highlight some of the active research being done by this group.

Singularity Handling The physical singularities inherent to black hole solutions pose a critical problem to those who wish to use standard finite differencing techiques and they must handled by coordinate choices, puncture techniques, or singularity excision.
	Formulation of the Einstein Equations The very form in which the equations are written has a drastic impact upon the stability of any evolution, and this is doubly true here. Over the past few years interest has risen steadily in careful analysis of the formulation of the Einstein equations.
Binary Black-Hole Initial Data Any evolution scheme begins with a specification of initial data. Our use of excision techniques for singularity handling allows us to use natural superposed Kerr-Schild-type data, conditioned by a constraint solver, as our starting point. We have produced different variants on this superposition scheme, with desirable near- and far-field limits.
	Binary Black-Hole Collisions Beginning with superposed initial data, we are testing the limits of newer evolution schemes (e.g., BSSN) to evolve a strong-field binary collision in full 3D, through the formation of a common apparent horizon, and towards the "ringdown" regime.

Apples With Apples Penn State is a participant of the "Apples with Apples" project, for comparing different numerical codes, and devising useful tests for successful NR codes. A results page is maintained here.