Extension of General Relativity

Abstract

Abstract Nonlocal general relativity (GR) requires an extension of the mathematical framework of GR. Nonlocal GR is a tetrad theory such that the orthonormal tetrad frame field of a preferred set of observers carries the sixteen gravitational degrees of freedom. The spacetime metric is then defined via the orthonormality condition. The preferred frame field is used to define a new linear Weitzenböck connection in spacetime. The non-symmetric Weitzenböck connection is metric compatible, curvature-free and renders the preferred (fundamental) frame field parallel. This circumstance leads to teleparallelism. The fundamental parallel frame field defined by the Weitzenböck connection is the natural generalization of the parallel frame fields of the static inertial observers in a global inertial frame in Minkowski spacetime. The Riemannian curvature of the Levi-Civita connection and the torsion of the Weitzenböck connection are complementary aspects of the gravitational field in extended GR.