Fermi coordinates in Schwarzschild spacetime: closed form expressions

Abstract

Fermi coordinates are constructed as exact functions of the Schwar\-zschild coordinates around the world line of a static observer in the equatorial plane of the Schwarzschild spacetime modulo a single impact parameter determined implicitly as a function of the latter coordinates. This illustrates the difficulty of constructing explicit exact Fermi coordinates even along simple world lines in highly symmetric spacetimes.

arXiv comment16 pages, 3 figures; published version

References in corpus (8)

• The evolution of circular, non-equatorial orbits of Kerr black holes due to gravitational-wave emission
• Complete analytic solution of the geodesic equation in Schwarzschild--(anti) de Sitter space--times
• Analytic solutions of the geodesic equation in higher dimensional static spherically symmetric space-times
• Precise relativistic orbits in Kerr and Kerr-(anti) de Sitter spacetimes
• Compact calculation of the Perihelion Precession of Mercury in General Relativity, the Cosmological Constant and Jacobi's Inversion problem
• Explicit Fermi Coordinates and Tidal Dynamics in de Sitter and Goedel Spacetimes
• Kerr metric, static observers and Fermi coordinates
• Exact Fermi coordinates for a class of spacetimes

Cited by in corpus (8)

• The Dirac equation in general relativity, a guide for calculations
• Deviation and precession effects in the field of a weak gravitational wave
• Fritz Hasenohrl and E = mc^2
• All order covariant tubular expansion
• Fermi coordinates and static observer in Schwarzschild spacetime
• Relativistic Tidal Accelerations in the Exterior Schwarzschild Spacetime
• Jacobi Fields and Tidal Effects in Kerr Spacetime
• General Construction of Tubular Geometry