General Transformation Formulas for Fermi-Walker Coordinates

TL;DR

This paper derives explicit Taylor expansion formulas for transforming arbitrary coordinates to Fermi-Walker coordinates around timelike paths in general spacetimes, including coefficients and Jacobian matrices.

Contribution

It provides the first explicit formulas for coordinate transformations to Fermi-Walker coordinates in arbitrary spacetimes, including their Jacobians.

Findings

Explicit Taylor expansion formulas for transformations and inverse transformations.

Formulas for coefficients and Jacobian matrices in Fermi-Walker coordinates.

Applicable to general spacetimes and arbitrary timelike paths.

Abstract

We calculate the transformation and inverse transformation, in the form of Taylor expansions, from arbitrary coordinates to Fermi-Walker coordinates in tubular neighborhoods of arbitrary timelike paths for general spacetimes. Explicit formulas for coefficients and the Jacobian matrix are given.