Numerical Relativity and Black-Hole Collisions

In four lectures I review numerical techniques for solving the Einstein equations on supercomputers, with application to colliding black hole spacetimes. There are two parts to the lectures: (1) numerical relativity and parallel computing, and (2) evolving black-hole spacetimes. In the first part, I describe the astrophysical motivation behind this work, the formulation of the equations for numerical relativity, slicing and gauge conditions, numerical techniques for solving the equations, and general coding and parallel computing issues. This is a general guide to developing codes to solve the Einstein equations. In the second part I focus on an application of the techniques discussed previously to black-hole spacetimes. I discuss black-hole initial-data sets and their construction, coordinate choices for the initial data and evolution, boundary conditions and apparent horizon techniques, event-horizon finders and applications, and recent progress in this area.