Gravitation as Anholonomy

TL;DR

This paper explores the concept of gravitation as anholonomy of tetrad fields, emphasizing the teleparallel approach where torsion represents gravitational field strength, and discusses implications for inertial and accelerated frames.

Contribution

It clarifies the relationship between gravitation, anholonomy, and torsion within the teleparallel framework, highlighting the role of tetrad fields and Lorentz transformations.

Findings

Torsion corresponds to gravitational field strength in teleparallel gravity.

Anholonomic frames are necessary for accelerated observers.

Electromagnetic fields appear with additional terms in accelerated frames.

Abstract

A gravitational field can be seen as the anholonomy of the tetrad fields. This is more explicit in the teleparallel approach, in which the gravitational field-strength is the torsion of the ensuing Weitzenboeck connection. In a tetrad frame, that torsion is just the anholonomy of that frame. The infinitely many tetrad fields taking the Lorentz metric into a given Riemannian metric differ by point-dependent Lorentz transformations. Inertial frames constitute a smaller infinity of them, differing by fixed-point Lorentz transformations. Holonomic tetrads take the Lorentz metric into itself, and correspond to Minkowski flat spacetime. An accelerated frame is necessarily anholonomic and sees the electromagnetic field strength with an additional term.