Tensor-Tensor Theory of Gravitation

TL;DR

This paper develops a tensor-tensor gauge theory of gravity, introducing a new tensor field as a translation gauge field, leading to modified gravitational effects, solutions with novel properties, and potential implications for cosmology and black hole physics.

Contribution

It proposes a novel tensor-tensor gauge theory of gravity with a translation gauge field treated as a Higgs-Goldstone field, resulting in new solutions and physical predictions.

Findings

Massive translation gauge field yields Yukawa-like correction to Newtonian potential.

Existence of a singular surface inside Schwarzschild radius prevents gravitational collapse.

String-like solutions may cause Aharonov-Bohm effects for spinless particles.

Abstract

We consider the standard gauge theory of Poincar\'{e} group, realizing as a subgroup of $GL(5. R)$. The main problem of this theory was appearing of the fields connected with non-Lorentz symmetries, whose physical sense was unclear. In this paper we treat the gravitation as a Higgs-Goldstone field, and the translation gauge field as a new tensor field. The effective metric tensor in this case is hybrid of two tensor fields. In the linear approximation the massive translation gauge field can give the Yukava type correction to the Newtons potential. Also outer potentials of a sphere and ball of the same mass are different in this case. Corrections to the standard Einshtein post Newtonian formulas of the light deflection and radar echo delay is obtained. The string like solution of the nonlinear equations of the translation gauge fields is found. This objects can results a Aharonov-Bohm type effect even for the spinless particles. They can provide density fluctuations in the early universe, necessary for galaxy formations. The spherically symmetric solution of the theory is found. The translation gauge field lead to existence of a impenetrable for the matter singular surface inside the Schwarzschild sphere, which can prevent gravitational collapse of a massive body.