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We review recent results on inverse problems for the wave equation in an (n + 1)-dimensional space equipped with a pseudo-Riemannian met- ric with Lorentz signature and discuss conditions for the existence of black (white) holes for these wave equations. We prove energy type estimates on a finite time interval in the presence of black or white holes. These estimates are used to prove the nonuniqueness in inverse problems.

Uniqueness and Nonuniqueness in Inverse Hyperbolic Problems and the Black Hole Phenomenon