Tensor-tensor model of gravity

Abstract

The main problem with the standard gauge theory of the Poincaré group realized as a subgroup of GL(5, R) is that fields, whose physical sense is unclear, appear in connection with the non-Lorentz symmetries. Here, the Poincaré fields are treated as new Yang-Mills-type tensor fields and gravity is treated as a Higgs-Goldstone field. In this case, the effective metric tensor for matter is a hybrid of two tensor fields. In the linear approximation, the massive translation gauge field gives the Yukawa-type correction to the Newtonian potential. Also, corrections to the standard Einstein post-Newtonian formulas for light deflection and radar echo delay are obtained. A spherically symmetric solution to the equations of translation gauge fields is also found. The translation gauge field leads to the existence of a singular surface, which is impenetrable to matter and can prevent gravitational collapse of a large body, inside the Schwarzschild sphere.