An algorithm for computing geometric relative velocities through Fermi and observational coordinates
arXiv:1301.2932 · doi:10.1007/s10714-013-1623-9
Abstract
We present a numerical method for computing the \textit{Fermi} and \textit{observational coordinates} of a distant test particle with respect to an observer. We apply this method for computing some previously introduced concepts of relative velocity: \textit{kinematic}, \textit{Fermi}, \textit{spectroscopic} and \textit{astrometric} relative velocities. We also extend these concepts to non-convex normal neighborhoods and we make some convergence tests, studying some fundamental examples in Schwarzschild and Kerr spacetimes. Finally, we show an alternative method for computing the Fermi and astrometric relative velocities.
21 pages, 11 figures, revised version with some comments and a figure added
References in corpus (10)
- Equatorial circular motion in Kerr spacetime
- Fermi coordinates, simultaneity, and expanding space in Robertson-Walker cosmologies
- General Transformation Formulas for Fermi-Walker Coordinates
- Lightlike simultaneity, comoving observers and distances in general relativity
- On Doppler tracking in cosmological spacetimes
- Relative velocities for radial motion in expanding Robertson-Walker spacetimes
- A note on the computation of geometrically defined relative velocities
- Kinematic relative velocity with respect to stationary observers in Schwarzschild spacetime
- Maximal Fermi charts and geometry of inflationary universes
- A physical interpretation of Hubble's law and the cosmological redshift from the perspective of a static observer