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Seasonal greetings, good tidings I bring, the end is not nigh............ not ever!
Note correction to the third Equation 16/1/14
The state of the universe has bothered me for some time, according to the majority view its full of black holes and every black hole will eventually develop a singularity in its core and these will eventually gobble up everything and either coalesce into one big one or slowly drift apart forever, either way it looks like curtains for all life eventually if singularities form. Anything falling into a singularity gets pulped down to zero size. A nasty end for life the universe and everything.
However conventional theorists seem to have ignored the radius excess which develops inside massive objects. The formula for radius excess comes from Feynman's work on Einstein's General relativity, it appears as the second equation here. It makes things bigger on the inside than on the outside like Dr Who's Tardis. However we only tend to notice the effect for very massive objects.
From this second equation I derive the third, which gives the radius of a hypersphere for any mass. An object meets the hypersphere (3-sphere) condition when the radius excess makes the internal radius swell to one quarter of the external circumference. the formula gives the external radius and it comes out at about one third of the event horizon or Schwarzchild radius, see the first equation.
Now a hypersphere will resist any further implosion under its own gravity as its angular velocity already equals lightspeed according to my neo-Gödelian formula for its vorticitation ('rotation' through its fourth dimension), see the fourth equation.
It doesn't matter too much at first if you fall into a black hole if its a really huge one that doesn't curve spacetime too sharply, the problems start when you begin to fall into a central singularity.
However the third equation shows that black holes will actually contain hyperspheres not singularities, and it doesn't matter if your planet or spaceship falls into one of these so long as its sufficiently huge not to give rise to the sort of spacetime curvature that would shred matter near a singularity or a small black hole.
In fact our universe consists of just such a very huge hypersphere with a correspondingly gentle spacetime curvature that we barely notice on the small scale.
Thus the universe cannot end in singularities (and neither did it begin with one, buts that's another story I've told elsewhere).
So DO NOT PANIC, black holes will form, but without singularities. If life can keep itself out of the way of the smaller ones and wait till a really vast one becomes available to enter then it can survive indefinitely for hyperspheres will eventually merge into ever vaster ones refreshing the universe by becoming the universe.
Well I hope that cheers everyone up this season, my apologies to Penrose and Hawking for destroying the singularity theorem, but they really should have taken Feynman's radius excess into account.