Light Bending Effect

Spin_Network
In GR the bending of light around a Large Mass produces a Gravitational Lensing effect.

I have a gedanken, I have a light source that has a finite 'ridgid' beam, a L.A.S.E.R beam. I point the beam into the night sky, at a location to the far West Horizon. I now proceed to arc the beam across the sky, to the farthest location in the East Sky Horizon.

Q)Does the swift motion of my arm cause the Beam's ridgidity to produce a drag "bending" effect?, similar to such as here:http://www.maths.soton.ac.uk/staff/Andersson/gwastro/sld016.htm [Broken]

In the image at the left, the spacetime lines which all 'bend' inwards towards the BH. For light travelling along these lines, the light would be bent inwards, a Gravitational Bending of Light.

Now in my above L.A.S.E.R light gedanken, I would not see any bending by the beam because of my proximity to the source, UNTIL I move my arm across the sky! I would definitly see a Drag-Effect in the beam.

I am always aligned with the beam, as I am directly at source. But surely another observer some distance away, close to the Beams directional path, will observe a "bending" of the beam? For instance, if the image above is used purely for "effect", choose any line upon the grid, move away from the Blackhole, it's curveture would become more rigid, the lines would automatically strighten out, gradually one's path is fixed towards the Light Source.

Ok, but if the Blackhole is in a high transit, if it was travelling at speed across space, then as with my Laser Beam, its effect of light bending would produce a lot of curveture in not just the Local Space, but Space far..far away.

Can this effect real within GR?..can observers outside the line of sight, of both source, me and laser, and Blackhole, conclude that there is a geniune warping of Light in any given intervening Space?

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