We study the perturbations of two classes of static black ellipsoid solutions of four-dimensional vacuum Einstein equations. Such solutions are described by generic off-diagonal metrics which are generated by anholonomic transforms of diagonal metrics. The analysis is performed in the approximation of small eccentricity deformations of the Schwarzschild solution. We conclude that such anisotropic black hole objects may be stable with respect to the perturbations parametrized by the Schrodinger equations in the framework of the one-dimensional inverse scattering theory. [References: 21]
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