  We study black holes for the linear hyperbolic equations describing the wave
propagation in the moving medium. Such black holes are called artificial since
the Lorentz metric associated with the hyperbolic equation does not necessary
satisfies the Einstein equations. Artificial black holes also arise when we
consider perturbations of the Einstein equations. In this paper we review
author's results of [E2] and [E3] on the existence and the stability of black
holes for the stationary wave equations in two space dimensions, and in the
axisymmetric case.
