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

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

2000-10-26

arxiv.org/abs/gr-qc/0010096v1

Class.Quant.Grav. 16 (1999) 465-477

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

LATeX, 13 pages

Scientific paper

10.1088/0264-9381/16/2/011

We obtain the integral formulae for computing the tetrads and metric components in Riemann normal coordinates and Fermi coordinate system of an observer in arbitrary motion. Our approach admits essential enlarging 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 plane-wave metric in Fermi normal coordinates.

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