question about gravitational lensing

[SRH]

Due to gravitational lensing, from a starlight behind a massive body, the light will bend around the object forming an arc.

My questions are:
1. Has gravitational lensing been observed with a massive body that is rotating rapidly, and is there an observed "break" in the arc at the rotational axis of the rotating body?
In other words, over the rotational axis, is the arc either less luminous or non-existent?
Perhaps this has not been observed with the Moon, but the Moon does not rotate that fast.

2. What is the reason for multiple (4) arcs forming, such as in the Einstein Cross (rather than 3, or 5, or 6 arcs)?


Thanks.

[antoniseb]

...
1. Has gravitational lensing been observed with a massive body that is rotating rapidly, and is there an observed "break" in the arc at the rotational axis of the rotating body? In other words, over the rotational axis, is the arc either less luminous or non-existent? ...

I assume you mean with the lensing body being the rapid rotator, not the lensed body. The answer is that we've never observed what you are asking about, and probably never will. We do stand a chance of observing some Lens-Thirring effects when we can see detail slightly smaller than the event horizon of Sgr A*, but that will be a lot more complicated than "a break".

As to your Einstein Cross question, the strict Einstein Cross situation involves a point source (almost) perfectly aligned with a nearly spherical source gravity. Arcs come from whole galaxies smeared out but are often seen through clusters with more complicated positioning of the mass.

[ngc3314]

To add a bit to antoniseb's point - a background source directly behind a mass distribution with spherical symmetry along the line of sight yields an Einstein ring (if it is distant enough behind the lensing mass). Slight misalignments will change the uniformity of the ring, giving two unequal and opposite maxima. A greater misalignment will yield two separate and opposite images, distorted into pieces of the Einstein ring. If the mass distribution is not circularly symmetric, the Einstein ring becomes asymmetric, so that substantial misalignments often yield 4 bright pieces. This happens either for nonspherical elliptical galaxies, or disk galaxies (the Einstein Cross quasar, the Zwicky Cross galaxy/quasar 2237+030, and a large number of 4-image lenses from SDSS and HST surveys). Groups and clusters of galaxies can have even larger numbers of light paths reaching us from a distant source - there is the theta-shaped galaxy seen 5 times through the cluster 0024+2654, and the record as far as I know is a 6-image lens formed by a group of galaxies - B1359+154.

With all these even numbers of images, it is interesting that (as Bill Burke showed in a stunningly brief paper in the 1980s) topological arguments show that a nonsingular mass distribution always produces an odd number of images. However, it is very common for the third (fifth...) image to appear very close to the core of the lens system, and to be strongly demagnified rather than amplified (making it extremely hard to see).