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We develop the complete composite theory of gravity, in which the gaugevector fields of the Yang-Mills theory with Lorentz symmetry group areexpressed in terms of the tetrad variables obtained from the decomposition of ametric. A key element of a compelling formulation of composite gravity arerefined coordinate conditions that offer a natural coupling of thegravitational field to matter and ensure the closest relationship to generalrelativity. The composite theory of gravity is presented from three differentperspectives highlighting its intuitive interpretation, its relationship togeneral relativity and its canonical Hamiltonian formulation, where the latterclarifies the structure of the heavily constrained theory and provides thestarting point for its quantization. The main physical ingredient of the theoryis an anisotropic velocity-momentum relation, or tensorial mass, described by ametric. We discuss the static isotropic solution in great detail because itprovides the background for the high-precision tests to be passed by analternative theory of gravity and for the understanding of black holes.

A dynamically constrained Yang-Mills theory with Lorentz symmetry group as an alternative theory of gravity