Kerr metric, static observers and Fermi coordinates

TL;DR

This paper derives the coordinate transformation to Fermi coordinates for static and circularly orbiting observers in the Kerr spacetime, aiding local analysis of gravitational effects near rotating black holes.

Contribution

It provides a detailed derivation of Fermi coordinates for static and orbiting observers in Kerr spacetime, extending previous work to more general observer motions.

Findings

Explicit Fermi coordinate transformations for static observers.

Extension of Fermi coordinates to uniformly circular orbiting observers.

Enhanced tools for local gravitational analysis in Kerr spacetime.

Abstract

The coordinate transformation which maps the Kerr metric written in standard Boyer-Lindquist coordinates to its corresponding form adapted to the natural local coordinates of an observer at rest at a fixed position in the equatorial plane, i.e., Fermi coordinates for the neighborhood of a static observer world line, is derived and discussed in a way which extends to any uniformly circularly orbiting observer there.