Gravity as a Yang-Mills Theory Based on the Lorentz Group

Abstract

The Yang-Mills theory associated with the restricted Lorentz group is revisited as a candidate for a theory of gravity. This is a natural idea because the principle of equivalence of gravitation and inertia suggests to introduce locally inertial coordinate systems with the gauge freedom of Lorentz transformations. Compared to previous implementations of the idea, we use a generalized expression for the vector potential of the gauge theory in terms of the metric, which involves a coupling constant. One can verify that, in the limit of small coupling constant, all the classical predictions of general relativity are reproduced. For the resulting higher-order field equations, the nature of the singularity associated with black holes changes. The proposed theory is based on a dimensionless action for coupling the Yang-Mills field to matter.