Stationary black hole metrics and inverse problems in two space dimensions
We study the wave equation for a stationary Lorentzian metric in the case of two space dimensions. Assuming that the metric has a singularity of the appropriate form, surrounded by an ergosphere which is a smooth Jordan curve, we prove the existence of a black hole with a boundary (called the event horizon) that is piecewise smooth, generally having corners. We consider a physical model of acoustic black hole whose event horizon has corners. Finally we consider the determination of a black hole by the boundary measurements.