Modeling Gravitational Wave Collapse into Black Holes

Einstein's field equations are a complicated set of nonlinear, coupled partial differential equations. Their nonlinear nature makes them very difficult to solve analytically. One way to sidestep these difficulties, is to linearize these equations and consider the corresponding "weak field" solutions. Taking such solutions as approximate initial data for a full numerical evolution can provide insight into the nonlinear self-interaction of gravitational waves. We present a numerical evolution of the collapse of time symmetric waves and present black hole collapse and dissipation of these waves. We describe the beginnings of a search for the threshold of black hole formation and critical behavior in the collapse of these gravitational waves.