Aberration by gravitational lenses in motion

Abstract

It is known that a fully relativistic integration of the null geodesics of a weak perturbation of flat spacetime leads to a correction of order $v/c$ to the bending angle and time delay due to a gravitational lens in slow motion with small acceleration. The existence of the $v/c$ correction was verified by the VLBI experiment of the bending of light by Jupiter on September 8, 2002. Here the $v/c$ correction is interpreted by means of standard aberration of light in an optically active medium with an effective index of refraction induced by the gravitational field of a lens in motion.Comment: 3 page

On gravitational lensing by deflectors in motion

“…Just as for a stationary space–time, where Fermat's principle exactly holds, even if the lens is in slow motion, the bending angle α and the gravitational time delay, Δ T pot =Δ T −Δ T geo , can be related by a gradient (Frittelli 2003b), where ∇ ⊥ ≡∇− e in ( e in ·∇). The bending angle turns out to be Once again, three terms contribute to α .…”

“…Hereafter, in this section, the primed coordinates will refer to the rest frame. A rigid motion along a path γ can be accounted for by a change of coordinates x ′→ x = x ′+ γ ( t ′) (Frittelli 2003b). Limiting to negligible acceleration of the path, the change in the time coordinate is such that (Frittelli 2003b).…”

“…A rigid motion along a path γ can be accounted for by a change of coordinates x ′→ x = x ′+ γ ( t ′) (Frittelli 2003b). Limiting to negligible acceleration of the path, the change in the time coordinate is such that (Frittelli 2003b). The metric takes the same form as in with where .…”

“…Various authors have investigated the problem of light deflection by lenses in motion. The effect of a translational motion of the deflector on a static background has been widely discussed (Pyne & Birkinshaw 1993; Kopeikin & Schäfer 1999; Frittelli 2003a,b; Heyrovsky 2004; Wucknitz & Sperhake 2004), and an early disagreement on the correction factor of first order in velocity has been solved [see Wucknitz & Sperhake (2004), and references therein]. Gravitational lensing by spinning deflectors has been also addressed with very different approaches (Epstein & Shapiro 1980; Ibáñez & Martin 1982; Ibáñez 1983; Dymnikova 1986; Glicenstein 1999; Ciufolini et al 2003; Sereno & Cardone 2002; Sereno 2002, 2003a,b, 2005).…”

Gravimagnetism, causality, and aberration of gravity in the gravitational light-ray deflection experiments

“…Equation (29) transforms coordinates in the gravity field equations (13), (14) while equation (30) transforms coordinates in the Maxwell equations. It is important to observe that in the limiting case of a very slow velocity v the spatial part of the two boosts (29) and (30) is reduced to two Galilean transformations [59] that are not identical because c g = c. Specifically, equation (29) yields…”