Velocity addition formulas in Robertson-Walker spacetimes
arXiv:1503.05208 · doi:10.1063/1.4926352
Abstract
Universal velocity addition formulas analogous to the well-known formula in special relativity are found for four geometrically defined relative velocities in a large class of Robertson-Walker spacetimes. Explicit examples are given. The special relativity result is recovered as a special case, and it is shown that the spectroscopic relative velocity, in contrast to three other geometric relative velocities, follows the same addition law as in special relativity for comoving observers in Robertson-Walker cosmologies.
arXiv comment26 pages, 5 figures
References in corpus (18)
- The IAU 2000 resolutions for astrometry, celestial mechanics and metrology in the relativistic framework: explanatory supplement
- The fundamental definition of 'radial velocity'
- Explicit Fermi Coordinates and Tidal Dynamics in de Sitter and Goedel Spacetimes
- Intrinsic definitions of "relative velocity" in general relativity
- Fermi coordinates, simultaneity, and expanding space in Robertson-Walker cosmologies
- General Transformation Formulas for Fermi-Walker Coordinates
- Exact Fermi coordinates for a class of spacetimes
- Lightlike simultaneity, comoving observers and distances in general relativity
- Recessional velocities and Hubble's law in Schwarzschild-de Sitter space
- Superluminal velocities in Schwarzschild-de Sitter space
- Relativistic simultaneity and causality
- Relative velocities for radial motion in expanding Robertson-Walker spacetimes
- Decelerating cosmologies are de-scramblers
- A note on the computation of geometrically defined relative velocities
- Maximal Fermi charts and geometry of inflationary universes
- Kinematic relative velocity with respect to stationary observers in Schwarzschild spacetime
- Reconstructing the velocity field beyond the local universe
- An algorithm for computing geometric relative velocities through Fermi and observational coordinates