Weitzenb\"ock's Torsion, Fermi Coordinates and Adapted Frames

Abstract

We study Weitzenb\"ock's torsion and discuss its properties. Specifically, we calculate the measured components of Weitzenb\"ock's torsion tensor for a frame field adapted to static observers in a Fermi normal coordinate system that we establish along the world line of an arbitrary accelerated observer in general relativity. A similar calculation is carried out in the standard Schwarzschild-like coordinates for static observers in the exterior Kerr spacetime; we then compare our results with the corresponding curvature components. Our work supports the contention that in the extended general relativistic framework involving both the Levi-Civita and Weitzenb\"ock connections, curvature and torsion provide complementary representations of the gravitational field.