6533b820fe1ef96bd127a41f
RESEARCH PRODUCT
A note on the computation of geometrically defined relative velocities
Vicente J. Bolóssubject
PhysicsMathematics - Differential GeometryPhysics and Astronomy (miscellaneous)General relativityComputationOpen problemRelative velocityFOS: Physical sciences83C99 53B30Observer (special relativity)KinematicsGeneral Relativity and Quantum Cosmology (gr-qc)General Relativity and Quantum CosmologyClassical mechanicsDifferential Geometry (math.DG)FOS: MathematicsTest particleAstrophysics::Galaxy AstrophysicsFermi Gamma-ray Space Telescopedescription
We discuss some aspects about the computation of kinematic, spectroscopic, Fermi and astrometric relative velocities that are geometrically defined in general relativity. Mainly, we state that kinematic and spectroscopic relative velocities only depend on the 4-velocities of the observer and the test particle, unlike Fermi and astrometric relative velocities, that also depend on the acceleration of the observer and the corresponding relative position of the test particle, but only at the event of observation and not around it, as it would be deduced, in principle, from the definition of these velocities. Finally, we propose an open problem in general relativity that consists on finding intrinsic expressions for Fermi and astrometric relative velocities avoiding terms that involve the evolution of the relative position of the test particle. For this purpose, the proofs given in this paper can serve as inspiration.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2011-09-01 |