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We study the wave equation for a stationary Lorentzian metric in the case oftwo space dimensions. Assuming that the metric has a singularity of theappropriate form, surrounded by an ergosphere which is a smooth Jordan curve,we prove the existence of a black hole with the boundary (called the eventhorizon) that is piece-wise smooth, generally having corners. We consider aphysical model of acoustic black hole whose event horizon has corners. In theend of the paper we consider the determination of a black hole by the boundarymeasurements.

Stationary Black Hole Metrics and Inverse Problems in Two Space Dimensions