Critical behavior of gravitational collapse in vacuum space-times

Einstein's equations are notoriously difficult to solve analytically. One approach to finding solutions is to linearize them, find solutions in this simpler setting and use such solutions as approximate initial data for solving the full Einstein equations numerically. We do exactly this. We consider quadrupole gravitational waves from an isolated source. Initial data is created parametrizing these waves which are then evolved in full GR using an existing numerical relativity framework called Dendro-GR. Using this approach we begin an investigation of critical behavior in the collapse of vacuum gravitational waves. Varying only the initial wave amplitude, we perform a bisection search to hone in on the critical solution. Our approach for discerning collapse vs dispersion focuses on the lapse, the collapse of which becomes a good indicator of the formation of a horizon.