Using the Fedosov theory of deformation quantization of an endomorphism bundle we construct several models of pure geometric, deformed vacuum gravity, corresponding to an arbitrary symplectic noncommutativity tensor. Deformations of Einstein-Hilbert and Palatini actions are investigated. Coordinate covariant field equations are derived up to the second order of the deformation parameter. For some models they are solved and explicit corrections to an arbitrary Ricci-flat metric are pointed out. The relation to the theory of the Seiberg-Witten map is also studied and the correspondence to the spacetime noncommutativity described by the Fedosov Ã-product of functions is explained.

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It is shown how Seiberg-Witten equations can be obtained by means of Fedosov deformation quantization of endomorphism bundle and the corresponding theory of equivalences of star products. In such setting, Seiberg-Witten map can be iteratively computed for arbitrary gauge group up to any given degree with recursive methods of Fedosov construction. Presented approach can be also considered as a generalization of Seiberg-Witten equations to Fedosov type of noncommutativity.

Model of noncommutative gravity is constructed by means of Fedosov deformation quantization of endomorphism bundle. The fields describing noncommutativity -symplectic form and symplectic connection -are dynamical, and the resulting theory is coordinate covariant and background independent. Its interpretation in terms of Seiberg-Witten map is provided.Also, new action for ordinary (commutative) general relativity is given, which in the present context appears as a commutative limit of noncommutative theory.