QUESTION: Dr. Nelson,
I have been reading a certain question in which you are directing a student on how to model colliding black holes. It amazes me that someone in just high school can even contemplate undertaking such a project. Anyways, to my question. Could you explain to me how exactly such a project works? I find the idea very interesting and I was wondering what exactly modeling a black hole in water does. Laymen's terms would be best because I am only an amateur at this kind of stuff.
ANSWER: Keep in mind, this is not some exact model of a black hole. It shares qualitative similarities, however, which I thought he might find interesting. Obviously, one cannot collide black holes in the laboratory. The math alone for actual physical modeling of black holes requires experience in not only differential equations and tensor algebra, but with using them in the context of general relativity.
That said: to the similarities. If we just wished to look at objects falling into a black hole, we might start by considering that drag forces are usually proportional to velocity. So we could imagine dropping small objects of near-neutral buoyancy into the water near the opening of a thin tube. The tube would be sucking in water, and providing a force. The velocity of the water will increase as the object approach the tube proportional to 1/r^2, where r is the distance to the opening. So the force of the water on nearby objects is much like the force of gravity in the neighborhood of the black hole (not accounting for the extreme warping of spacetime right near the black hole's event horizon itself). Small particles in the water (I experimented and suggested pepper flakes and possibly a little soap in the water to help keep them from sticking to the surface tension) could be filmed and tracked. Since black holes can have angular momentum, I suggested that the water return line have some kind of vortex-inducing tip on it, so water coming in toward the intake itself could then have some angular momentum. Locally, this would result in a relatively fixed angular momentum to the stretching space around it, corresponding to some level of internal angular momentum for the black hole coupled with the now-observed (experimentally) frame dragging.
That's the basis of the model of one black hole on the behavior of the space around it. It's not a perfect model. Colliding the black holes would simply require building an identical system and literally bringing the intakes close enough together to attract one another. Adjusting the relative angles of the return lines (and thereby the directions of angular momentum of the colliding black hole) is a possible experimental parameter which can be varied in hopes of viewing interesting phenomena on the video of the "collision." Results will be difficult to predict in advance without detailed mathematical models, but possibly explainable in a more qualitative sense.
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QUESTION: So you're saying that the force of the water intake could simulate forces similar to that of the gravitational pull of a black hole? Would there be any way to get quantitative information from that?
That, then becomes the complex part. Since you said you wanted things in layman's terms and that you're an amateur...I'll leave it that you can get quantitative data out of it, but it's only an approximation of what would happen with black holes and you don't want to get into something that complex as trying to translate between the two.