Fermi-Frenet coordinates for space-like curves

We generalize Fermi coordinates, which correspond to an adapted set of coordinates describing the vicinity of an observer's world line, to a coordinate system in a neighbourhood of the worldsheet of an arbitrary spatial curve in a static spacetime. The spatial coordinate axes are fixed using a covariant Frenet triad, analogous to that of classical differential geometry, so that the metric can be expressed in terms of the curvature and torsion of the spatial curve. This construction is used to analyze the covariant definition of inertial forces felt by an observer constrained to motion upon the worldsheet. We also consider the application of these coordinates to examining photon propagation in arbitrarily-curved optical fibres.