If a particle were to escape from one black hole, the intense curvature of spacetime in this configuration would virtually guarantee that it would be absorbed by one of the other black holes eventually. Note that the Schwarzschild Radii of these supermassive black holes are continuously expanding and the conditions for a particle to escape the gravitational pull of a singularity at exactly the Schwarzschild Radius are as follows:
* It must move at the speed of light
* It must travel in a direction directly perpendicular to the surface of the event horizon.
Under these gravitationally "crowded" conditions your particle would be very lucky to escape at all and even luckier to avoid the other black holes. It would be like the old adage, "out of the frying pan into the fire."
Your black hole idea has merit if you stick completely to the math. Here are the operating concepts:
1) A black hole is mathematically defined as a singularity. As far as this universe is concerned a black hole is a theoretical point - no width, height, or depth. See http://en.wikipedia.org/wiki/Gravitational_singula rity
2) "Space" in it's purest form is that which is defined by at least four non-coplanar points. This is the basis for special relativity. See http://en.wikipedia.org/wiki/Minkowski_space
Those with any physics background should immediately see where I'm headed but I'll spell it out for mere mortals. Consider the model of the universe as theorized in the article. Regardless of how long it takes and discounting any effects of Hawking radiation, everything will eventually fall into a black hole. Imagine a dance of supermassive black holes stripping each other's accreation disks and eventually combining one into another as their orbits about their common gravitational centers degrade. The most massive of the black holes will behave much like cosmic vacuum cleaners as their Schwarzschild Radius expand and atttract their brethren.
Given that the model of the universe as theorized in the article hold true (which happens to be THE assumption in this exercise) we will start to realize the mathematical death of the universe. Consider the final four supermassive black holes in the universe have eaten everything else as exist in a non-coplanar configuration in Minkowski space. We say that in the presence of gravity, spacetime is described by a curved 4-dimensional manifold for which the tangent space to any point is a 4-dimensional Minkowski space. Under these conditions there is only one possible tangent and the concept of the "spatial curvature" of general relativity falls away since all space is now Minkowski space.
Here's where the math starts getting interesting.
I'll state this as the Wikipedia article so eruditely expressed:
"An orthonormal basis for Minkowski space necessarily consists of one timelike and three spacelike unit vectors. If one wishes to work with non-orthonormal bases it is possible to have other combinations of vectors. For example, one can easily construct a (non-orthonormal) basis consisting entirely of null vectors, called a null basis."
This is precisely what we have in the final dance of the four supermassive black holes -- the final orthonormal basis. When two of the final four combine then we need to consider space to be collapsing by a dimension. We are now in a flat universe. When the two remaining combine we are in a one-dimensional universe.
When the final two mate, we have the inner product of the remaining vector = 0. Which relativity considered "lightlike" and we've lost the tensor basis for gravity.
All of the mass of the universe converted to pure energy and gravity rendered meaningless.
Big bang.
What I consider to be the really interesting physics is at that moment of cosmic singularity we have no "timelike" vectors left. Is that an artifact of the math breaking down and not describing the physics or is it and effective paradox to the the model of the universe as theorized in the article?
Your claims would really mean something if you had posted some PROOF. If that were true it would really be something to stuff in the $oftie's faces. My only problem is that I see these interesting tidbits here and bring them up in "discussions" elsewhere only to be shown, without doubt, that many are simply untrue.
Slashdot Mirror
* It must move at the speed of light
* It must travel in a direction directly perpendicular to the surface of the event horizon.
Under these gravitationally "crowded" conditions your particle would be very lucky to escape at all and even luckier to avoid the other black holes. It would be like the old adage, "out of the frying pan into the fire."
1) A black hole is mathematically defined as a singularity. As far as this universe is concerned a black hole is a theoretical point - no width, height, or depth. See http://en.wikipedia.org/wiki/Gravitational_singula rity
2) "Space" in it's purest form is that which is defined by at least four non-coplanar points. This is the basis for special relativity. See http://en.wikipedia.org/wiki/Minkowski_space
Those with any physics background should immediately see where I'm headed but I'll spell it out for mere mortals. Consider the model of the universe as theorized in the article. Regardless of how long it takes and discounting any effects of Hawking radiation, everything will eventually fall into a black hole. Imagine a dance of supermassive black holes stripping each other's accreation disks and eventually combining one into another as their orbits about their common gravitational centers degrade. The most massive of the black holes will behave much like cosmic vacuum cleaners as their Schwarzschild Radius expand and atttract their brethren.
Given that the model of the universe as theorized in the article hold true (which happens to be THE assumption in this exercise) we will start to realize the mathematical death of the universe. Consider the final four supermassive black holes in the universe have eaten everything else as exist in a non-coplanar configuration in Minkowski space. We say that in the presence of gravity, spacetime is described by a curved 4-dimensional manifold for which the tangent space to any point is a 4-dimensional Minkowski space. Under these conditions there is only one possible tangent and the concept of the "spatial curvature" of general relativity falls away since all space is now Minkowski space.
Here's where the math starts getting interesting.
I'll state this as the Wikipedia article so eruditely expressed:
"An orthonormal basis for Minkowski space necessarily consists of one timelike and three spacelike unit vectors. If one wishes to work with non-orthonormal bases it is possible to have other combinations of vectors. For example, one can easily construct a (non-orthonormal) basis consisting entirely of null vectors, called a null basis."
This is precisely what we have in the final dance of the four supermassive black holes -- the final orthonormal basis. When two of the final four combine then we need to consider space to be collapsing by a dimension. We are now in a flat universe. When the two remaining combine we are in a one-dimensional universe.
When the final two mate, we have the inner product of the remaining vector = 0. Which relativity considered "lightlike" and we've lost the tensor basis for gravity.
All of the mass of the universe converted to pure energy and gravity rendered meaningless.
Big bang.
What I consider to be the really interesting physics is at that moment of cosmic singularity we have no "timelike" vectors left. Is that an artifact of the math breaking down and not describing the physics or is it and effective paradox to the the model of the universe as theorized in the article?
You be the judge.
Your claims would really mean something if you had posted some PROOF. If that were true it would really be something to stuff in the $oftie's faces. My only problem is that I see these interesting tidbits here and bring them up in "discussions" elsewhere only to be shown, without doubt, that many are simply untrue.