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.
Cite
@article{arxiv.1502.04183,
title = {Weitzenb\"ock's Torsion, Fermi Coordinates and Adapted Frames},
author = {Donato Bini and Bahram Mashhoon},
journal= {arXiv preprint arXiv:1502.04183},
year = {2015}
}
Comments
17 pages, revtex macros, 2 pictex figures; v2: slightly expanded version accepted for publication in Phys. Rev. D; v3: typos corrected