Kemplerer rosettes and black holes

Factual Questions
1

Before I say anything else I want to say very clearly I am a biologist. My education in physics runs to failing the A level and reading most of “a brief history of time”. Therefore if I have misunderstood anything important and this is all complete rubbish I apologise for wasting your time.

Anyway I recently read Larry Nivens ringworld, this book describes five planets locked together in a Kemplerer rosette. That is an arrangement of planets at the points of an equilateral polygon, the gravitational fields of each planet holding the other planets into position at a set distance away from each other. This sounds plausible (I have heard of Lagrangian points and such) and I have a vague idea I have come across the idea somewhere else before.

My question(s) is this – If such an arrangement can work with planets then why not black holes. Presumably if identically sized black holes where placed (or created) in precisely the right positions this arrangement could hold them very close together. If this is indeed the case.

  1. how stable would such an arrangement be . I would assume only a slight increase in the size of one of the singularities would cause the whole thing to collapse.
  2. What are the potential effects of having such massive objects close to each other (I keep meaning to write some science fiction some day and this struck me as a passably bad pseudoscience way to create a wormhole).
  3. Would it be possible for an object to approach the arrangement through the area of opposing gravitational pull and pass in and out of the area that would normally be within the black holes event horizons.
  4. Are there any other arrangements in which this would work, I presume the idea would work in 3D and not just on a plane.
2

Everything I know about these things comes from this page: http://burtleburtle.net/bob/physics/kempler.html

Note the spelling should be Klemperer, not Kemplerer

3

Oh, Eris, look at the last animation.
Those black holes of yours would absorb one another pretty sharp.
Before long they would start swapping Hawking radiation, falling ito each other’s gravity well, probably radiating energy by gravity waves …
and once their event horizons touch, you have one black hole, not two. Mind you, do it right and you could end up with a rapidly spinning black hole, which have some possible interesting phenomena inside-
pity there’s no way out of a black hole to tell the tale…

SF worldbuilding at
http://www.orionsarm.com/main.html

4

Are the instabilities demonstrated in the link inevitable if the system is perfectly balanced and not effected by outside factors. I know this would likely be impossible in actuality, but I didn’t think that was the sort of thing that put off physicists :slight_smile: . Would the system be more stable or less stable if it wasn’t moving ?
Can anyone be more specific about how this would relate to black holes in paticular (or at least make a wild guess).

Thanks

5

WAG: I’m guessing, given the discussion of Lagrange points, that the Klemperer Rosettes are phenomena characteristic of a Newtonian gravity. With black holes, general relativistic corrections will become important extremely quickly, and energy loss to gravitational waves would also become important relatively quickly. Thus, none of the configurations would be stable, even with a perfect setup.

If the systems were not moving, they wouldn’t work at all. In the 5-object ring, the 5 moons are orbiting the center of gravity of the 5 moon system. If they’re not moving, they’re not orbiting, and thus will just quickly crash together.