..without jumping in, of course...
this is one of the questions where i'm not that sure..
is there any mathematical proof ?
I know there are some alternative ideas, but i heard it was shown that there must be a singularity
So can someone please be so kind and shed some light onto this ? ;)
Mercury 2010
Favorite Answer
check some of my previous answers and you might find some info to help you.
http://physics.syr.edu/courses/modules/LIGHTCONE/schwarzschild.html
looks like this its an equation by Schwarzschild and endorsed by Einstein.
here ya go
The singularity at r = 1 in the Schwarzschild space-time metric
$ds^2= (1 - 1/r)dt^2-\frac {dr^2} {(1-1/r)}- r^2(d\theta ^2 + \sin^2 \theta d\phi^2)$
is investigated from a physical standpoint.
http://links.jstor.org/sici?sici=0080-4630(19650126)283%3A1395%3C491%3ATSITSS%3E2.0.CO%3B2-F
Tim C
technically it might not be a singularity, it could be just a bit smaller than the event horizon itself. the only "proof" we have of a singularity in a black hole is that at that extreme gravitational region, no known force can stop gravity, so the matter must collapse into a singularity, but we do not absolutely know this for sure, maybe there is some other force that we have not found yet.
mathematician
The only way to do a mathematical proof is to assume that, say, general relativity holds. Unless you have the physics understood, you won't be able to mathematically prove anything.
What has been shown is that, under general relativity, certain situations inevitably lead to singularities (Hawking and Penrose proved these). The conditions around some collapsing stars are good enough for these theorems to apply. Of course, since we don't know how quantum mechanics affects general relativity, our conclusions do not take such things into consideration.
Professional Physicist
without gettiing in to the philosphy of "proof"....the singularity is purely a mathematical construct having infinite density and zero "size". A quantum theory of gravity is needed before a more realistic model of black holes is formed. More likely there is a new state of matter at the centre of black holes...no singularity.
johnandeileen2000
The term,"singularity," is ill defined if there can be more than one of them. There are many black holes, as a matter of fact they are quite common. If mathematical was available to prove otherwise it would have been published by now.