Tensor-tensor model of gravity

The main problem with the standard gauge theory of the Poincaré group, realized as a subgroup of $GL(5,R)$, is the appearance of fields connected with non-Lorentz symmetries and whose physical sense is unclear. In this paper, we treat the Poincaré gauge fields as new, Yang–Mills-type tensor fields and gravity as a Higgs–Goldstone field. In this case, the effective metric tensor for matter is a hybrid of two tensor fields. It is shown that in the linear approximation, the massive translation gauge field can give the Yukava-type correction to Newton's potential. Also, corrections to the standard Einstein post-Newtonian formulae for light deflection and radar echo delay are obtained. A spherically symmetrical solution to the equations of translation gauge fields is found. The translation gauge field leads to the existence of a singular surface inside the Schwarzschild sphere that is impenetrable to matter and can prevent gravitational collapse of a massive body.