Expert: Courtney Seligman - 4/1/2010

Question
How exactly do black hole singularities form, when considering the effects of the zero gravity core of a forming black hole?  That is, as a black hole is about to form, there will also be a center of gravity, that the black hole is attempting to collapse into, where the newton shells of mass around the center of gravity obviously have no gravitational effect on the center of gravity core.  Even if the outer shells of matter are under a gravitation acceleration faster than light at the shells, I can't tell from the unit analysis, due to temporal dilations, what exactly happens about the core, as the mass shells contract.  I can see that the core ranges from zero gravity, at the exact center of gravity, to light speed accelerations around the infalling matter shells.  As the outer matter shells fall in, under acceleration forces faster than light, it compresses the low gravity normal core, increasing its temperature, blasting the infalling matters with their energy, slowing their fall.  As the spheres of outer matter falls, the inner portions hit this hot core and are blown outward, and other shells fall in, that are also pushed outward.  At steady state, I can see a potential final core of superheated matter supporting a thin sphere of matter against falling in equilibrium.  Physicists say black holes form singularities, but I have never seen the zero gravity "belly button" of black hole formation addressed as to how it collapses and interacts with the infalling black hole quarrantined matter.

Answer
(Sorry for the delay in answering. I had an appointment this morning, and just picked this up.)

Although you are correct in that the center of a normal object has zero weight (because there is nothing between it and the center), it is still held in place by the weight of the material above. This is true for any object which is larger than the Schwarzschild radius for its mass (about 2 miles radius per solar mass, if I recall correctly).

However, once the object becomes smaller than the Schwarzschild radius, two factors change the situation. First, the presumption that at the center you are "weightless", because there is no mass between you and the center, becomes less and less accurate, as the material surrounding the core compresses it. After all, even if there were no mass exactly at the center, if you had, say, a solar mass within a few inches of the center, the weight of that mass, pushing down on the core, would be nearly infinite. And when the singularity does form, all the mass IS in the center, and the gravity IS infinite.

Of course, as you say (I've rarely gotten a question with so good an argument -- you obviously understand the basic principles very well), there would be a considerable outward pressure, due to the energy created by the compression of the infalling material. But although you propose that this pressure could somehow overcome the gravitational force, that is wrong. In fact, that's the whole idea of the Schwarzschild radius.

To see how this works, suppose that you have an object that is very slightly expanding and contracting, as a result of imperfections in the balance between the compressional force of gravity, and the expansion force due to the pressure inside it. As the object compresses, work is done, increasing the heat of the object, and the pressure associated with its heat and density. That increase in pressure overcomes the greater gravity caused by the compression, expanding the object back to its original size. (At least, that's the way fluctuations in pressure and gravity normally work.)

HOWEVER, if the object is smaller than the Schwarzschild radius, you run into a problem. Namely, the energy required to expand the object becomes greater than the rest-mass energy of the object. It is important to realize this, as we could suppose that in addition to the forces we are familiar with, other forces might exist, which we are not aware of, because they only come into play under conditions so extreme that we have never encountered them. And if such forces could exist, and could be provided with the motive power required to overcome the gravitational compression, then black holes need not exist... EXCEPT...

As noted at the start of the previous paragraph, once something is compressed to less than the Schwarzschild radius, the energy required to do the work required to expand it back to that size is greater than any energy that you can create, by any means whatsoever, because even annihilating the entire mass of the object would not give you enough energy to accomplish that goal. The result is, that once something compresses to less than that size, even if there were some way of more or less stabilizing it at some smaller size, even the smallest fluctuation in its situation would inevitably compress it to smaller and smaller sizes. This would be true even if you ignore the momentum the infalling matter had, to start out. If you take that into account, an object compressing past that size would reach zero size and become a singularity in a very short period of time (fractions of a second, for stellar-mass black holes). But even if the object was close to equilibrium as it shrank or fluctuated in size, once it was smaller than the Schwarzschild radius it would be doomed to collapse to zero size in a very short period of time.

To summarize:
(1) Although for normal size objects, you can treat the regions near the center as being weightless, for "black holes", this is not true. The force compressing the core becomes nearly infinite, as the object gets closer and closer to zero size.

(2) Once an object is smaller than its Schwarzschild radius, no force can counteract gravity, because there isn't enough energy available, even by total annihilation of the object's mass, to overcome any "inward" fluctuations. So once an object contracts past that radius, it is doomed to shrink to zero size in practically no time at all.