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A new method of construction of integral varieties of Einstein equations inthree dimensional (3D) and 4D gravity is presented whereby, under correspondingredefinition of physical values with respect to anholonomic frames of referencewith associated nonlinear connections, the structure of gravity field equationsis substantially simplified. It is shown that there are 4D solutions ofEinstein equations which are constructed as nonlinear superpositions of solitonsolutions of 2D (pseudo) Euclidean sine-Gordon equations (or of Lorentzianblack holes in Jackiw-Teitelboim dilaton gravity). The Belinski-Zakharov-Meisonsolitons for vacuum gravitational field equations are generalized to variouscases of two and three coordinate dependencies, local anisotropy and mattersources. The general framework of this study is based on investigation ofanholonomic soliton-dilaton black hole structures in general relativity. Weprove that there are possible static and dynamical black hole, black torus anddisk/cylinder like solutions (of non-vacuum gravitational field equations) withhorizons being parametrized by hypersurface equations of rotation ellipsoid,torus, cylinder and another type configurations. Solutions describing locallyanisotropic variants of the Schwarzschild-- Kerr (black hole), Weyl(cylindrical symmetry) and Neugebauer--Meinel (disk) solutions with anisotropicvariable masses, distributions of matter and interaction constants are shown tobe contained in Einstein's gravity. It is demonstrated in which manner locallyanisotropic multi-soliton-- dilaton-black hole type solutions can be generated.Comment: revtex, twocolumns, 24 pages, version 3 with minor correction

Anholonomic Soliton-Dilaton and Black Hole Solutions in General Relativity