RAR, 3/3/00, revised 7/21/04
What Is Inside A Neutron Star, Quark Star, Black Hole?
Is a black hole a mathematical singularity or does it contain a finite-sized structure? This is not a trick question. Stephen Hawking originally proposed that black holes were literally "Out of This World", but he has just changed his mind! Other scientists have developed very complicated physical theories about what kind of matter is inside a black hole. But there is no way of checking these theories because everything goes into the event horizon radius of a black hole and nothing comes back out, except gravity!
So let us develop a new conceptual model of what must be inside a black hole based upon what we already know about other physical bodies that we see in nature. Let's look at atoms, then collapse them in a supernova to a neutron star, and then collapse them again to something even smaller called a quark star, and then to a black hole. Finally, let's see if it it is possible to destroy a black hole completely!
We have a very good model of the atom. It is made up of a central core of tightly packed neutral neutrons and positively charged protons, that are essentially incompressible spheres called nucleons, surrounded by a cloud of negatively charged orbital electrons. This inner core is called the nucleus. The electrons are much smaller, and about 2000 times less massive than the nucleons, and they stay relatively far away from the nucleus.
The nucleons each attract one another by short-range forces called the "strong force". Since protons are positively charged, they repel each other by Coulomb or "electrostatic force", which goes approximately as the square of the nuclear charge. There are usually more neutrons than protons in the nucleus, because the neutrons act like glue and hold the nucleus together against the strong Coulomb repulsion between nearby protons. The size of the nucleus is proportional to the number of nucleons in the nucleus, and is of the order of 10-13 cm.
If there are too many neutrons or protons, the nucleus is unstable and the excess nucleons are successively converted to the other type by beta decay or positron decay, accompanied by emission of an appropriate extra particle, called a neutrino, which carries off some of the decay energy. We think of this decay, due to nucleon imbalance, as being caused by the "weak force", which otherwise produces a type of incompressibility of each nucleon. The fourth type, or "gravitational force", is also present, but it is at least 30 orders of magnitude smaller than the nuclear forces and plays no role in the ordinary behavior of an atom.
The electrons travel in essentially circular orbits around the nucleus, but these orbits are quantized, which means that only certain orbits are allowed and the energy levels are discrete. Niels Bohr developed the Classical theory governing electron orbits. The negatively charged electrons in the inner orbits have to have a great deal of kinetic energy so that their centrifugal force balances the Coulomb attraction from the nucleus. The electrons in the outer orbit have energies of only a few electron volts. The latter are called valence electrons, and they are responsible for the chemical properties of the atom. The diameter of the atom is determined by the outer orbit, and is of the order of 10-8 cm. Hence, an atom is mostly empty space, since the nucleus is 5 orders of magnitude smaller than the atom, and the electrons are infinitesimal! Molecule sizes are determined by the combined outer diameters of two or more atoms because only the outer electron orbits overlap.
There is one other nuclear decay mode that should be mentioned, called electron capture. In quantum mechanics, the electron orbits are not fixed circles, but rather are probabilities that the electron or its wave equivalent will be located in a certain place in space. For some unstable nuclei, the inner orbit has a finite probability of overlapping the nuclear volume, and occasionally the electron combines with a proton to form a neutron, thus effectively causing decay. An analogous process is discussed in the next section.
Supernova Type-II Core Collapse
A supernova is the explosion of a dying star. Gravity causes the gas and other matter in a star to collapse toward the center of the star. Resistance to collapse is produced by the random thermal motions of the hot gasses in the star's interior, which provide an outward pressure that counterbalances the gravitational attraction. These gasses are heated by energy released by fusion reactions. Fusion occurs for light elements up to but not including iron. Hence, when everything but iron has been used up in the center of the star, it can no longer produce enough heat energy to hold off collapse and the iron atoms pack tighter and tighter together.
"Gravitational force" is the weakest of the four fundamental forces, but it can have a tremendous effect if a great deal of matter is packed closely enough together. In this case, the external gravitational pressure on the packed core forces the electron orbits in the iron atoms to move closer to the nucleus until the extra centrifugal force balances the outside pressure. But if there is enough external pressure, the inner shell electrons can hit the nuclear surface and undergo forced electron capture. We call this point the Chandrasekhar limit, where the degenerate electron pressure due to Pauli exclusion fails, which occurs for a core of about 1 1/2 solar masses. The next shell electrons rush inward, so that even more electrons hit the nucleus. The result is a catastrophic collapse of the atom as all of the space occupied by the electron orbits suddenly disappears. It is calculated that the center of the star reduces its diameter by 10,000 times in about 1/10 of a second!
The above time of collapse is inconsistent with the only time-related experimental measurement from supernova SN1987A. Approximately 20 neutrinos were detected in a 12 second time span, so the collapse may actually be of the order of seconds.
Here is where I have difficulty with the accepted theory of what happens next. The conventional idea is that some of the inward-directed energy of gravitational collapse is converted to an outward-directed shock wave, and this wave is then heated by neutrinos emitted during electron capture, resulting in enough outward-directed energy to blow the outer layers of the star away in a gigantic explosion.
It would seem to me that once core-collapse occurred, it would continue unabated as the gravitational force got stronger and stronger and pulled all the matter towards the center! The central core would get hot, but it is hard to see how this could produce any significant outward motion against the strong gravitational attraction.
But this is at odds with the observed fact that the star explodes! So we need a new explanation. Clearly, the explosion would be much easier to explain if some of the mass was converted to energy by some sort of a fission process, because we know that atom bombs produce very large explosions in this manner.
Now, it is an accepted fact that a Supernova Type-I gaseous star explodes like a hydrogen bomb using the fusion reaction. The problem for scientists is that a Supernova Type-II doesn't contain any more fusion fuel, but what about an unconventional fissionable fuel? We shall leave for later a suggestion of what that fuel might be!
Regardless of how the supernova explosion proceeds, the net effect of having all of the electrons in an atom captured by all of the protons is the production of a nucleus of pure neutrons! Since the entire thing is neutral, there is no longer any electromagnetic force, although the other three forces continue to act. The result of packing a great many pure neutron "atoms" together is a gigantic crystal composed entirely of neutrons. The neutron crystal ash core, left over after the outer layers of a supernova have been blown away, is called a neutron star.
Since the original star had some spin, the collapsed neutron star would have to conserve angular momentum and spin very fast indeed. We call this rapidly spinning neutron star a pulsar, since pulsars were discovered by detection of their rapid radio-frequency emissions. Pulsars have been found accompanying many, but not all supernovae. It is not known if neutron stars are produced in all type-II supernovae, or whether the detection problem is one of being in the wrong place to make the observation. A pulsar can theoretically have a mass of no more than about 2 1/2 solar masses before the degenerate neutron pressure due to Pauli exclusion fails and it can no longer resist its own gravitational collapse to a black hole.
Quark Stars ?
In April 2002, it was reported that scientists using the Chandra X-ray observatory had discovered that two known neutron stars had unusual properties. One was too small and the other was too cold. If the measurements are correct, both have densities of the order of 5 times that of nuclear matter! The authors say that the neutrons must have shattered into "free" quarks and/or formed "strange" matter. But experiments at the Brookhaven Collider reported in 2004 seem to have produced a quark-gluon plasma with a density of at least 10 times nuclear density. So, additional space can indeed be squeezed out of nucleons!
One speculation is that the center region of these stars is composed of free quarks and the outside is formed of neutrons, although free quarks have never been observed. Alternately, some of the quarks may have been converted from up or down to strange, allowing them to form strange matter inside the star.
There is no adequate theory to cover the situation. In the Standard Model, a neutron is made up of two down quarks and one up quark, while a proton is made up of two up quarks and one down quark. The rest of the nucleon is made up of gluons that hold the nucleon together, and agraviton that gives the nucleon the property of gravity. Quarks may not be fundamental particles, because there are too many different types of them, unless the up and down quarks can be converted to the other types by excitation to higher energy levels! In this regard, the current favored theory to explain the deficit of neutrinos coming from the Sun is the "resonance" conversion of one type of neutrino to another by "vacuum energy".
Conceptually, we can think of a neutron or proton as being analogous to an atom in the sense that it is mostly empty space! An up quark and a down quark form a bound diquark combination with a net charge of +1/3. The down quark has a charge of -1/3, which makes the neutron neutral. The up quark has a charge of +2/3, which makes the proton +1. The odd quark and the diquark spin around each other much like the electrons spin around the nucleus, and the outward centrifugal force of motion balances the attraction of the gluons, to give the nucleon its size. Decay occurs when the odd single quark is triggered to change from up to down, or down to up, by the repulsive "weak force".
What happens when gravitational pressure is exerted on a neutron? The orbits of the diquark and down quark have to get smaller to resist the pressure. At some point the neutron structure has to fracture, and let the quarks merge into a triquark. At this point, another sudden volume reduction takes place.
My own feeling is that there is no such thing as a free quark, and recent experiments at the Brookhaven Super Collider seem to confirm that conclusion. I believe that all quarks are bound in doublets in mesons or triplets in baryons. The observed volume reduction of a quark star relative to a neutron star can then be explained by partial conversion of neutrons to triquarks in the center of the quark star where the gravitational pressure is the greatest.
Finally we come to a discussion of what might be inside a black hole. There are two possibilities. Either the complete conversion of all of the neutrons to triquarks may be sufficient to create a black hole, or some or all of the quarks must indeed be excited to the strange, etc., form creating a more compact bound structure.
The resulting internal black hole structure must be analogous to the structure of a neutron star! We must form some sort of a triquark or strange matter crystal, where the weak force provides the incompressibility. This crystal would occupy the central core of the black hole and contain all of the mass of the original structure and all of its gravity.
The Schwartzchild radius or event horizon is determined by the total amount of mass enclosed in the black hole. For mass only, the theoretical Schwartzchild solution  shows that this radius increases linearly with mass. In fact, the crystal in the center becomes bigger at a slower rate than the much larger event horizon. For a spinning black hole, the Kerr theoretical solution gives a radius that varies proportionally to mass and inversely to spin.
This structured crystal is what I believe is inside a black hole, rather than a mathematical singularity. All the matter is still there, crushed to the next lowest stable state of existence, with gravitational attraction balanced by incompressibility.
Finally, inside a black hole, space is not actually bent around on itself as Einstein predicts. Instead, light at speed c is attracted by gravity and its path is bent to travel around in a complete circle, giving the effect of total internal reflection. That is why the light cannot escape a black hole! Gravity does escape because it still travels in a straight line,
What Happens Next If We Keep Adding Mass?
The real question is, can this process of mass agglomeration continue indefinitely? If the universe collapsed to a single point, could all of its mass be contained in a single gigantic black hole, or is there another fracture point? Again, I believe that the answer is yes, there is a limit, and that is the point where the gravitons can no longer bind energy together to form matter. This is the equivalent to the limit of degenerate triquark pressure due to Pauli exclusion. When the gravitational pressure crosses this point, the quarks must be torn apart, and matter is converted to pure photon energy which transports away at the speed of light! Gravity ceases to exist, and the entity that formed the graviton is also released to travel away at the speed of light.
This new process may be the ultimate example of destruction and creation, the precursor to a new Big Bang! Energy and momentum have to be conserved, and all the ingredients are there in the proper proportions to create a new universe on the same scale as the old universe.
Read on in the accompanying articles for the details!
 W. J. Kaufmann, III, Black Holes and Warped Spacetime, W. H. Freeman and Company, 1979.