Riemann normal coordinates, Fermi reference system and the geodesic deviation equation

Abstract

We obtain the integral formulae for computing the tetrads and metric components in Riemann normal coordinates and the Fermi coordinate system of an observer in arbitrary motion. Our approach admits an essential enlarging of the range of validity of these coordinates. The results obtained are applied to the geodesic deviation in the field of a weak plane gravitational wave and the computation of the plane-wave metric in Fermi normal coordinates.