Gravity from Invariance Under Transformations of Minkowski Metric

The Minkowski manifold serves as the standard model of spacetime for relativistic theories of non-gravitating matter. It admits global coordinate systems and a Minkowski metric. In fact, it admits more than one Minkowski metric. In special relativity, one of these metrics is chosen as the non-dynamical physical metric. The theory is not invariant under a transformation that maps this metric to another Minkowski metric. We reformulate special relativity to make it invariant under such transformations by introducing a non-dynamical auxiliary tensor field. When we promote this field to be a dynamical gravitational field, the physical metric also becomes dynamical. To determine the dynamics of this field, we propose a three-parameter theory of gravity in which the spacetime manifold is a nonempty open subset of the Minkowski manifold. The action functional and the field equations of the theory are identical to the ones in New General Relativity, the theory of teleparallel gravity. In addition, the theory admits the traceless canonical energy momentum tensor of the gravitational field and the divergenceless total canonical energy momentum tensor. This leads to the divergenceless total energy and momentum vector currents and conserved total energy and momentum. The theory also admits the symmetric and divergenceless total energy momentum tensor.