Fermi-Frenet coordinates for space-like curves

TL;DR

This paper extends Fermi coordinates to space-like curves in static spacetimes using a covariant Frenet triad, enabling a clearer expression of inertial forces near arbitrary spatial curves.

Contribution

It introduces Fermi-Frenet coordinates for arbitrary spatial curves, generalizing existing Fermi coordinates and linking the metric to curvature and torsion of the curve.

Findings

Fermi-Frenet coordinates are applicable to space-like curves in static spacetimes.

Inertial forces can be expressed covariantly and intuitively using these coordinates.

The metric near the curve depends explicitly on curvature and torsion.

Abstract

We generalize Fermi coordinates, which correspond to an adapted set of coordinates describing the vicinity of an observer's worldline, to the worldsheet of an arbitrary spatial curve in a static spacetime. The spatial coordinate axes are fixed using a covariant Frenet triad so that the metric can be expressed using the curvature and torsion of the spatial curve. As an application of Fermi-Frenet coordinates, we show that they allow covariant inertial forces to be expressed in a simple and physically intuitive way.