Rigid covariance, equivalence principle and Fermi rigid coordinates:gravitational waves

TL;DR

This paper investigates the conditions under which Fermi coordinates can be constructed to be both rigid covariant and applicable to linear plane gravitational waves, enhancing understanding of coordinate systems in gravitational wave spacetimes.

Contribution

It derives conditions for Fermi coordinates to be rigid covariant and applies these to linear plane gravitational waves, linking coordinate construction with gravitational wave analysis.

Findings

Established conditions for rigid covariant Fermi coordinates.

Applied these conditions specifically to linear plane gravitational waves.

Provided insights into coordinate systems in gravitational wave spacetimes.

Abstract

For a given space-time and for an arbitrary time-like geodesic, we analyze the conditions for the construction of Fermi coordinates so that they are also rigid covariant. We then apply these conditions to linear plane gravitational waves.