Towards constraining of the Horava-Lifshitz gravities

Recently a renormalizable model of gravity has been proposed, which might be a UV completion of General Relativity (GR) or its infra-red modification, probably with a strongly coupled scalar mode. Although the generic vacuum of the theory is anti-de Sitter one, particular limits of the theory allow for the Minkowski vacuum. In this limit (though without consideration of the strongly coupled scalar field) post-Newtonian coefficients of spherically symmetric solutions coincide with those of the General Relativity. Thus the deviations from the convenient GR should be tested beyond the post-Newtonian corrections, that is for a system with strong gravity at astrophysical scales. In this Letter we consider potentially observable properties of black holes in the deformed Horava-Lifshitz gravity with Minkowski vacuum: the gravitational lensing and quasinormal modes. We have showed that the bending angle is seemingly smaller in the considered Horava-Lifshitz gravity than in GR. The quasinormal modes of black holes are longer lived and have larger real oscillation frequency in the Horava-Lifshitz gravity than in GR. These corrections should be observable in the near future experiments on lensing and by gravitational antennas, helping to constrain parameters of the Horava-Lifshitz gravity or to discard it.