Why does a black hole have a finite mass? I mean besides the obvious "it has to have finite mass or it would suck up the universe." A singularity is a dimensionless point in space with infinite density, if I'm not mistaken. If something is infinitely dense, must it not also be infinitely massive? How does a black hole grow if everything that falls into it merges into the same singularity, which is already infinitely dense?
 A: So everybody seems to fall into a logical trap here.
Black holes don't have infinite density at their singularity/center. This infinite density business is the physics way of saying that we don't know what is going on.
It gets even worse now that Higgs Boson/Field is apparently what gives particles their mass. If there are no particles in a Black Hole then what is there to interact with the Higgs Field to generate mass?
A: 
If something is infinitely dense, must it not also be infinitely massive? 

Nope. The singularity is a point where volume goes to zero, not where mass goes to infinity.
It is a point with zero volume, but which still holds mass, due to the extreme stretching of space by gravity. The density is $\frac{mass}{volume}$, so we say that in the limit $volume\rightarrow 0$, the density goes to infinity, but that doesn't mean mass goes to infinity.
The reason that the volume is zero rather than the mass is infinite is easy to see in an intuitive sense from the creation of a black hole. You might think of a volume of space with some mass which is compressed due to gravity. Normal matter is no longer compressible at a certain point due to Coulomb repulsion between atoms, but if the gravity is strong enough, you might get past that. You can continue compressing it infinitely (though you'll probably have to overcome some other force barriers along the way) - until it has zero volume. But it still contains mass! The mass can't just disappear through this process. The density is infinite, but the mass is still finite.
A: if it has infinite density, that would mean it has infinite gravity (or infinite space curvature in special relativity, which i believe in). so, it obviously doesn't have infinite density because that would suck the whole entire universe into itself. that would mean it would have to have an unmeasurably small amount of volume. and even if it did have infinite density, space curvature should be more powerful nearer to the singularity, but how can we add more to an infinite amount of gravity? if it had infinite density, its curvature should be equal everywhere, which is also impossible. What do you think of this theory?
A: A black hole has an infinite density; since its volume is zero, it is compressed to the very limit.  So it also has infinite gravity, and sucks anything which is near it!  Not everything  there is!!  Now above all when it sucks things it adds up to its mass, which remains finite and it always will, even if it did suck in the whole universe!!  It's all for the formula: density in a black hole is mass divided by volume (0) so the density is infinite, not the mass!!! So thus a black hole has mass which is finite and will always be finite.
A: I'm not going to claim any real knowledge on the topic, or most of what I bring up, so feel free to correct me for any extremely rash or impossible aspects, but here it goes.
A black hole to me, seems like it's just the epitomy of nothing.  There's something, then general space, and then a black hole.  It appears to me that something to nothing is relatively possible, as at one point nothing came to be something, however I feel that the universe itself wouldn't allow such a flaw, as the universe seems quite perfect in its design.  
One theory I've stumbled upon is a theory that all atoms have a negative and positive form of which they can swap between.  Kind of a matter and anti-matter deal, but all atoms experience this, and that we live in the positive.  
This kind of interacts with the idea of a black hole, a massive explosion of something that created energy to powers beyond numbers we have words for (googlplex's), for a length of years we barely use the number for (billions).  And it eventually explodes, and in the wake of such energy, a black hole is formed (If that's still what people believe).  So a rediculous mass of positive energy goes out from a point in the universe, and in this point, it sucks in mass, everything, a perfect unescapable gravity pit.  
Could it possibly be that after so much positive energy radiates from one point, it explodes, then begins sucking in all the positive energy that comes into it, to rebalance the rediculous amount of negative energy that would then be in the wake of such a thing?
I can kind of imagine it, more like an explosion under water (an implosion really).  First it explodes, and then everything gets sucked in until it's at its natural point.  Except this is on a massive (much bigger than any bomb we could ever make or imagine), yet scale so small (fills itself in to a sub-atomic level, if not to an electron level) it takes an unbelievably long time to go back to normal.
And even then that doesn't factor in to say that all this energy its taking in, isn't being vortex'd to another space or even time.
So, as a summary, I suppose what I'm concluding black holes to be, is an enormous sphere of negative.  And as all things want to be neutral, it sucks in as much positive (the reality we live in) as possible, practically, indefinitely, all positive matter that goes near it to be sucked in without flaw, no possible escape.  To anwser whether it has mass, I really don't know for sure, but from what I can tell, it has a Finite mass.  But the time required for it to reach a neutral point is absolutely rediculous, seeing as how it would have to fill all that space flawlessly, to the absolute with the little bit of energy that it gets coming in from light, or small fragments of atoms.
But again, I have no real knowledge on the topic, its just my educated guess on what I've read and learned over a little while.
