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 the boundary (called the event horizon) that is piece-wise smooth, generally having corners. We consider a physical model of acoustic black hole whose event horizon has corners. In the end of the paper we consider the determination of a black hole by the boundary measurements.