timmdeeg said:
Saying straight line, have you this scenario in your mind?
Star and two equally sized black holes form an equilateral triangle and on the opposite side the same with an observer instead of the star. Both triangles are in the same plane.
No. I was thinking of the photo's of the eclipsed sun taken by Eddington to help Einstein prove GR. Background star light passing near the sun appeared to move (displace) out since the light path was curved by curved spacetime. Since this pass-by effect is largely localized nearer the gravity source, but inversely lessened further away from the gravity source, I imagine it has the effect of "cratering" a "spacetime rim" of all nearby background light, including bright stars, into a concentrated ring of slightly brighter magnitude. I expect that this "rim" effect is an effect greatly magnified more rim-like by a powerful gravity source such as a BH as opposed to a sun-sized star. I did not mean the formal Chwolson Ring that Einstein once noted by any single bright star in a perfectly concentric sight line with the gravitational body.
By dim background glow, I mean that I believe the entire sky is evenly covered by nearly invisible direct distant starlight from somewhere (barring another BH dark spot). This very weak glow is then considered omni-present, but nearly obliterated by ordinary starlight as ordinary starlight is diminished by a bright moon. In the case of a very powerful gravitational lensing effect, I supposed that the "gathered" marginal rim-glow would become more detectable. And then finally, I thought that two nearby BH's would create a "double flat-tire effect" deforming the "crater rim light", which would then result in a squeezed straight line of starlight or flattened brighter tangent between them. Thus the expected general brighter line formation (or a proportional arc in the case of unequal BH's).
I my defense for answering like this, the original question itself was very general, seeming to look for a simple response, or observation. My post was what I thought to be an appropriate (though less than precise) simple expected answer. As we may note, the subject later morphed into a more detailed consideration (thread converted to "I") that seems to demand a graduate thesis quality answer, which is fine... as long as we differenciate the more precise, more complicated comparison as PeterDonis did above. The OP now knows his original question has no complete answer that is simple.
And, as far as the misspelling of Schwarzschild, my apologies... I normally watch my spelling. My Win7/I.E. 11 recently quit on this forum. I am now using a broken tablet that seems to have mind of it's own, and being lazy, did not check past duckduckgo.com which seemed to initially accept my misspelling. With all the misguided helpful tablet auto-corrects, outright errors and obliterations, I think I could write faster and more accurately on a stone tablet. :(
Wes