Fermi Coordinates for Weak Gravitational Fields

TL;DR

This paper derives a comprehensive Fermi coordinate system for observers in arbitrary motion within weak gravitational fields, extending previous models and clarifying the link between general relativity and Newtonian gravity.

Contribution

It provides a general derivation of Fermi coordinates applicable to any observer motion in weak fields, generalizing Rindler space for acceleration and rotation.

Findings

Derived Fermi coordinates valid to all orders in geodesic distance.

Connected general relativity with Newtonian gravity more precisely.

Extended Rindler space to arbitrary acceleration and rotation.

Abstract

A Reference is corrected. (We derive the Fermi coordinate system of an observer in arbitrary motion in an arbitrary weak gravitational field valid to all orders in the geodesic distance from the worldline of the observer. In flat space-time this leads to a generalization of Rindler space for arbitrary acceleration and rotation. The general approach is applied to the special case of an observer resting with respect to the weak gravitational field of a static mass distribution. This allows to make the correspondence between general relativity and Newtonian gravity more precise.)