Fermi-normal, optical, and wave-synchronous coordinates for spacetime with a plane gravitational wave

Understand

Fermi normal coordinates provide a standardized way to describe the effects of gravitation from the point of view of an inertial observer.

• These coordinates have always been introduced via perturbation expansions and were usually limited to distances much less than the characteristic length scale set by the curvature of spacetime.
• For a plane gravitational wave this scale is given by its wavelength which defines the domain of validity for these coordinates known as the long-wavelength regime.
• The symmetry of this spacetime, however, allows us to extend Fermi normal coordinates far beyond the long-wavelength regime.