Originally posted by twhitehead
Sure, but the question was 'what is the shape of the even horizon', not 'what will it be billions of years from now?'.
[b]It's a good thing you feel qualified to make a qualitative analysis of highly nonlinear, tensorial, differential equations without knowing anything about the subject. It really is.
It doesn't take detailed knowledge of the quan ...[text shortened]... ombination of singularities (at a distance) takes place? Wouldn't it violate relativity?[/b]
"t doesn't take detailed knowledge of the quantum equations of gravity to know that the earth is not currently on a collision course with the sun. "
😕. What does that has to do with anything?! 😕 By the way what are these so called quantum equations of gravity?
"It is patently obvious that your claim could not be valid without knowing the first thing about the equations."
😕
"Your claim was that the equations dictate that only one singularity can exist inside a given event horizon, but if two singularities are approaching, your claim would imply that as the event horizons touch, the singularities would instantaneously combine. I simply don't believe that that is the case. If you still maintain (with your apparently better knowledge of highly nonlinear, tensorial, differential equations) that that is the case then maybe you would care to explain how this instantaneous combination of singularities (at a distance) takes place? Wouldn't it violate relativity?"
Here you have some misconceptions and I'll do my best.
First of all is that Nature doesn't have to conform to what you, or I, think and/or believe.
My original claim was posed in the context of BHs that doesn't have a translational motion. And in that case the equations are very clear. only one singularity.
As for BHs that move and collide I didn't say anything because I don't know the first thing about it. Once again let me tell you GR equations are one of the hardest ones out there. I didn't pointed that out with the intention that saying I understand them much better than you (even though that would be a a natural thing to happen as I don't think you are a physicist), but only to point out that taking stands about the behaviour about the behaviour of BHs without a proper understanding of the equations is bound to fail.
The first thing that causes a lot of highly unintuitive behaviours is the fact that the equations are non-linear. Believe a lot of people that are way better than you and me in physics got wrong some qualitative answers to non-linear problems because they relied on natural intuition. As an example I can cite the Fermi-Pasta-Ulam problem. This was studied by those three guys in the first place (it was a simple and almost trivial non-linear problem) and they got it all wrong. Literally all wrong. The behaviour that they got was the complete opposite from what they expected. Of course that later things got worked out but it worked as an cautionary tale when dealing with non-linearities.
I refrain from doing any predictions to what will happen when two BHs collide, but I can tell you that if the two singularities merge in to one singularity SR isn't violated in any way. SR only prohibits faster that light travel when information is being transmitted. Since this will happen inside the event horizon, and no information is transmitted from inside the BH there is no violation. This analysis doesn't mean that the scneario is a certain one it only means that with our current day knowledge it isn't impossible.
Another point that I'd like to mention is that in Physics there are no holy grails. There will come the day that Sr will be violated and some new theory will be needed. That's just how things work in science.
I also made a google search and this is what came up:
As two galaxies merge, their supermassive black holes have to eventually interact. Either through a direct collision, or by spiraling inward until they eventually merge as well.
And that's when things get interesting.
According to simulations made by G.A. Shields from the University of Texas, Austin, and E.W. Bonning, from Yale University, the result is often a powerful recoil. Instead of coming together nicely, the forces are so extreme that one black holes is kicked away at a tremendous velocity.
http://www.universetoday.com/2008/02/29/what-happens-when-supermassive-black-holes-collide/
And this link also provide some information: http://news.cnet.com/Supercomputer-simulates-black-hole-collision/2100-11397_3-6062605.html
Just let me point out this:
Earlier trials failed since the equations based on Einstein's general relativity theory were so complicated that they made supercomputers crash. So back in the day even super computers crashed while trying to tackle this difficult problem.
I also found this. http://www.sciencedaily.com/releases/2006/04/060411080753.htm
But I can't seem to find no definite proposition to what happens to the two different singularities.