Olaf Wucknitz [1], Ulrich Sperhake [2]
We discuss a seeming inconsistency of relativistic light deflection with the classical picture of moving test particles by generalizing the lens effect to test particles of arbitrary velocity, including light as a limiting case. We show that the effect of radial motion of the lens is very different for slowly moving test particles and light and that a critical test particle velocity exists for which motion of the lens has no effect on the deflection angle to first order. An interesting and not immediately intuitive result is obtained in the limit of a highly relativistic motion of the lens towards the observer, where the deflection angle of light reduces to zero. This phenomenon is elucidated in terms of moving refractive media. Furthermore we discuss the dragging of inertial frames in the field of a moving lens and the corresponding Lense-Thirring precession, in order to shed more light on the geometrical effects in the surroundings of a moving mass.
In a second part we discuss the effect of transversal motion on the observed
redshift of lensed sources. We demonstrate how a simple kinematic calculation
explains the effects for arbitrary velocities of the lens and the test
particles.
Additionally we include transversal motion of the source and observer to
show that all three velocities can be combined into an effective relative
transversal velocity similar to the approach used in microlensing studies.
Key words:
PACS 95.30.Sf, 04.20.Cv, 04.25.Nx, 98.62.Sb
The first and second version are still available.
A
summary of this paper was presented in a conference talk and (slightly more
condensed) in a workshop talk.
Another paper on the subject was
submitted later.