Related papers: Velocity addition formulas in Robertson-Walker spa…
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…
Nature succeeds in accelerating extended and massive objects to relativistic velocities. Jets in Active Galactic Nuclei and in galactic superluminal sources and gamma-ray bursts fireballs have bulk Lorentz factors from a few to several…
An analysis of composite inertial motion (relativistic sum) within the framework of special relativity leads to the conclusion that every translational motion must be the symmetrically composite relativistic sum of a finite number of quanta…
The algebra of the relativistic composition of velocities is shown to be isomorphic to an algebraic loop defined on division algebras. This makes calculations in special relativity effortless and straightforward, unlike the standard…
The cosmological Robertson-Walker metric of general relativity is often said to have the consequences that (1) the recessional velocity $v$ of a galaxy at proper distance $\ell$ obeys the Hubble law $v=H\ell$, and therefore galaxies at…
A derivation of the relative velocity used in the definition of the relativistic cross-section is given in terms of manifestly Lorentz invariant quantities. Along the way we find that there is a certain arbitrariness in the usual definition…
The underlying geometri of spacetime algebra allows one to derive a force by contracting the relativistic generalization of angular momentum, M, with the mass-current, mw, where w is a proper 4-vector velocity. By applying this force to a…
Transformation rules for coordinates, velocities and accelerations in accelerated reference frames are derived. A generalized approach of the special relativity is taken for a basis. A 7-dimensional space including projections of velocity…
Doubly Special Relativity (DSR) is a class of theories of relativistic motion with two observer-independent scales. We investigate the velocity of particles in DSR, defining velocity as the Poisson bracket of position with the appropriate…
An accelerating flat universe with a variable cosmological term is obtained in the Robertson-Walker metric. The variable cosmological term is defined by the correction terms of the metric tensor field. Simple solutions of the scale factor…
The longitudinal Doppler shift is a measure of hyperbolic distance. Transformations of uniform motion are determined by the Doppler shift, while its square root transforms to a uniformly accelerated frame. A time-velocity space metric is…
Naively applying Hubble's law to a sufficiently distant object gives a receding velocity larger than the speed of light. By discussing a very similar situation in special relativity, we argue that Hubble's law is meaningful only for nearby…
We have defined a slowness, s, as the reciprocal conjugate of velocity, v. s = -ih/v. We have shown that Einstein's postulate (v has an upper limit) implies that s is discrete. A velocity operator is defined as the derivative with respect…
Generalized Robertson-Walker spacetimes extend the notion of Robertson-Walker spacetimes, by allowing for spatial non-homogeneity. A survey is presented, with main focus on Chen's characterization in terms of a timelike concircular vector.…
Doppler effect and Hubble effect in different models of space-time related to the space-time velocity of an observer are considered. The Doppler effect and Doppler shift frequency parameter are connected with the kinematic characteristics…
Relative motion in space with multifractal time (fractional dimension of time close to integer $d_{t}=1+\epsilon (r,t), \epsilon \ll 1$) for "almost" inertial frames of reference (time is almost homogeneous and almost isotropic) is…
We give a careful general relativistic and (1+3)-covariant analysis of cosmological peculiar velocities induced by matter density perturbations in the presence of a cosmological constant. In our quasi-Newtonian approach, constraint…
The Robertson-Walker (RW) metric allows us to apply general relativity to model the behavior of the Universe as a whole (i.e., cosmology). We can properly interpret various cosmological observations, like the cosmological redshift, the…
There have been a number of papers proposing that the light speed of a homogeneous and isotropic universe is variable. This paper outlines a simple way that the vectors and tensors of special relativity can be extended to allow such a…
A geometric construction for the Poincare formula for relativistic addition of velocities in one dimension was given by Jerzy Kocik in "Geometric Diagram for Relativistic Addition of Velocities", American Journal of Physics, volume 80, page…