Black holes , gravity upper limit

[Crazymechanic]

Now I thought about this while writing my "electric field strength ' question , as it was about has the electric field got an upper limit of strength and the answer is that it hasn't (theoretically)
then I thought the same thing about gravity.

Does gravity have an upper limit to it's strength or how strong it can get in a given area?

Now before I let you answer i want to express some of my thoughts that ,as much as I know according to GR it shouldn't have one but I'm not sure what QM has to say about it.
Theoretically shouldn't gravity have some kind of an upper limit which is dictated by the laws of QM , because as to my understanding ( maybe I'm missing something) if gravity would not have an upper limit then shouldn't a black hole keep on forever decreasing in size , even though as we know that gravity is the weakest of all the 4 forces in a black hole due to the mass present and the density of it gravity exerts a huge force on every other bit of mass thus creating a BH.
But once gravity has taken over the fusion /radiation pressure and all the other pressures left over from a star that has ended it's life cycle , shouldn't the gravity then continue to forever compress the matter that now forms a BH? Because if there is no upper limit for gravity then there also shouldn't be no stopping once it has taken over to the extent to which it doesn in a BH?
Ok these are my thoughts , now what's missing?

 

[SteamKing]

For the cores of dead stars, gravity isn't the only force at work. Although fusion has ceased, there are other quantum characteristics of matter which become significant when the squeeze is put on.

In a white dwarf, for example, the size of the star itself is limited by what is known as 'electron degeneracy pressure'. This is one result of the Pauli exclusion principle, which describes the allowable quantum states of matter. This EDP resists gravity, so the white dwarf reaches an equilibrium point.

In a neutron star, similar quantum considerations govern how much neutrons can be forced together. The details of the mechanism as yet are not completely understood, but if the neutron star's mass is below the Chandrasekhar limit, no further collapse can take place, unless additional mass is added to the star.

See:

http://en.wikipedia.org/wiki/Electron_degeneracy_pressure
http://en.wikipedia.org/wiki/Type_II_supernova

 

[Nugatory]

Does gravity have an upper limit to its strength or how strong it can get in a given area?

Not according to anything in general relativity. However GR is unlikely to work very well under conditions of very high curvature in very small areas for two reasons:
1) As you point out, it doesn't take quantum effects into consideration, and we know that these matter at sufficiently small scale.
2) GR allows for singularities, points at which GR cannot make any predictions . But if these singularities have physical significance, some theory has to work there. (Don't confuse these singularities, points at which the curvature of spacetime becomes undefined in GR, with mere "coordinate" singularities in which there's nothing wrong with the curvature, just a problem in the convention we use for describing it. The singularity at the center of a black hole is real, the one at the event horizon is just an artifact of using Schwarzschild coordinates).

But once gravity has taken over the fusion /radiation pressure and all the other pressures left over from a star that has ended it's life cycle , shouldn't the gravity then continue to forever compress the matter that now forms a BH? Because if there is no upper limit for gravity then there also shouldn't be no stopping once it has taken over to the extent to which it doesn't in a BH?

That is pretty much (except for the bolded part, which I don't understand - we cannot look inside the event horizon of the black hole to see what is or is not happening there) what GR says about the central singularity of a black hole.

However, in view of #1 and #2 above, it is much more likely that there is some upper limit to the gravitational force around the central point, so something else more sensible happens. However, it will take a theory of quantum gravity, something that hasn't been discovered yet, to predict what that upper limit will be.

 

[Crazymechanic]

Well , in the bold part i made a typo and i was not exactly clear as I should have been.
I meant that if gravity would have no upper limit and matter no phenomenon like pauli exclusion etc then it could go on and compress everything into a indefinitely small point which doesn't sound like reality or a real scenario given the other laws that govern the universe as we know it.

Yes I have heard of neutron degeneracy pressure and those other phenomenon.
Now if it weren't for those properties of particles/matter would then the gravity be able to compress particles into a mind boggling point of "non existence"?
I guess it's rather a theoretical "possible scenario" question rather than a science unsolved problem or a science question at all.

 

[pervect]

General relativity predicts that there won't be anything to stop the collapse of a black hole. There are logical extensions to GR that don't have this issue. In particular Einstein-Cartan theory (look for papers by Nikodem J. Popławski in particular) is one example of a theory that gets rid of these issues. Whether or not it's a correct theory is a different issue.

So the status is that there are theories that are currently experimentally indistinguishable from GR that don't predict total gravitational collapse to a point singularity. Unfortunately, the key assumptions of such theories are not directly testable with current technology (and I'm not sure they're testable with forseeable technology).

So basically, it doesn't make any difference to anything we can currently measure.