General Transformation Formulas for Fermi-Walker Coordinates

Abstract

We calculate the transformation and inverse transformation, in the form of Taylor expansions, from arbitrary coordinates to Fermi-Walker coordinates in tubular neighborhoods of arbitrary timelike paths for general spacetimes. Explicit formulas for coefficients and the Jacobian matrix are given.

23 pages. Corrected typos in the last two equations. Accepted for publication in Classical and Quantum Gravity

References in corpus (9)

• Fermi Coordinates for Weak Gravitational Fields
• Black hole tidal problem in the Fermi normal coordinates
• Explicit Fermi Coordinates and Tidal Dynamics in de Sitter and Goedel Spacetimes
• Energy-momentum tensor for a Casimir apparatus in a weak gravitational field
• Kerr metric, static observers and Fermi coordinates
• Riemann Normal Coordinates, Smooth Lattices and Numerical Relativity
• On the construction of Fermi-Walker transported frames
• A Statistical Mechanical Problem in Schwarzschild Spacetime
• A simple criterion for nonrotating reference frames

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