Black Holes: How does a three dimensional object collapse into a singularity & Where does the matter go?

A black hole comes into existence as the result of the core collapse of enormous stars, which lose quite some mass in a supernova explosion. However, supermassive black holes are still by any means hugely massive.

However, the theory still tells us the object is actually collapsed to a point/singularity at the core. If the object is to be a point, the mass must have gone somewhere? Is it all converted to energy and spewed out in gamma ray bursts etc? (and if so, what forms a black hole's mass? Is it just all in that point?)

Am I perhaps conceptually wrong and does the singularity only express a point of infinite gravity with matter whirling around beyond our observational capacity past the event horizon?

• Not sure of your question. You are asking about the mass. The entire mass of the star collapses into a single point. It doesn't 'go' anywhere. – Gummy bears Dec 5 '14 at 5:53

There are frameworks in physics, dimensional and energetic frameworks.

There is the classical framework which has classical theories of mechanics and electrodynamics etc, where the dimensions are compatible with the meters/seconds/kilograms measures.

There is the quantum framework which has quantum mechanics, quantum electrodynamics and quantum field theory. Its framework is in dimensions less than a nanometer and energies compatible with h_bar~1*10^-34 J second .

There is the special relativity framework adjacent to the quantum mechanical framework

There is the general relativity framework for dimensions in light years and masses of the order of stars.

Each framework is mathematically modeled with differential equations and solutions to these differential equations. The potentials and the solutions because of the nature of mathematical equations can have singularities.

For example the 1/r potential of classical electricity and magnetism leads us that at r=0 there exists a singularity for the classical problem. No hydrogen atom. But to go to r=0 the dimensions go to less than a nanometer, and the appropriate framework is the quantum mechanical framework, and lo and behold there are no singularities and we have the atom in a stable quantum state.

When a general relativity solution gives a singularity, again the dimensions go to the framework of quantum mechanics. It has no meaning to worry in terms of general relativity. Unfortunately the gravitational field has not been consistently quantized, there exist effective field theories but still one cannot know what happens at the corresponding r=0 . One can handwave with the heisenberg uncertainty principle, but until there exists a consistent theory of quantized gravity the statement is "we do not know what happens at the singularity", we expect that soon the theory will be extended so that a quantized model of gravity will apply and there will no longer be a singularity in the classical sense.

In the Big Bang model effective quantization has been introduced immediately after the general relativity solution singularity, with the inflaton field , and the cosmic microwave data fit the model. Patience, the mills of physics may grind slowly but they grind exceedingly fine.

The simple answer is that general relativity does not, and indeed cannot, tell us what happens to the matter when it is all compressed into the singularity.

We commonly describe black holes using the Schwarzschild metric because it's a relatively simple metric. However the Schwarzschild metric only describes the end result and doesn't tell us anything about how the black hole formed. The closest we have to an analytical description of black hole formation is the Oppenheimer-Snyder metric that describes a collapsing ball of dust. As the ball collapses the density increases, and as the ball approaches the singularity the density increases towards infinity.

The problem is that the Oppenheimer-Synder metric is singular at the singularity, just like the Schwarzschild metric. That means the metric cannot describe what happens at the singularity. We can approach the singularity as closely as we want, and as we do so the ball of dust becomes more and more dense. However we can't calculate what happens at the singularity itself.

The obvious interpretation is that at the singularity all the matter is still there, it's just compressed into a point of zero volume and infinite density. However I must emphasise that no-one believes this actually happens. We expect quantum gravity to become important at these very high densities and small sizes, and we expect quantum gravity to prevent the density becoming infinite. Sadly we have no theory of quantum gravity, so no-one knows exactly what happens to the matter.

• John, see arxiv.org/abs/1003.1359 where you can read that "Oppenheimer and Snyder found in 1939 that gravitational collapse in vacuum produces a "frozen star", i.e., the collapsing matter only asymptotically approaches the gravitational radius (event horizon) of the mass, but never crosses it within a finite time for an external observer." – John Duffield Jul 24 '15 at 17:53
• @JohnDuffield: I'm familiar with the Oppenheimer-Snyder metric and indeed have discussed it in several questions on this site. The OS metric becomes singular in finite proper time. It is certainly true that in the coordinates used by an external observer the horizon will never form, but that just takes us back to the old nothing can ever pass through an event horizon claim. If you were sitting on the surface of the collapsing star then you would merge with the singular in a finite time as measured by your wristwatch. – John Rennie Jul 24 '15 at 17:56
• Only that measurement hasn't happened yet, and it never ever will. Your proper time is merely some cumulative count of the vibrations of a piezo-electric crystal. And at the event horizon, all electromagnetic phenomena grind to a halt. Forever. Note the first paragraph of Eddington-Finkelstein coordinates on Wwiki. As for the event horizon, the frozen-star black hole can be likened to a hailstone. You're a water molecule, and you can't pass through the surface. But after you alight upon the surface, you get surrounded and buried by other water molecules. So the surface passes through you. – John Duffield Jul 25 '15 at 5:58
• @JohnDuffield: you are of course welcome to your own interpretation of these matters, however when I am answering questions for people who may one day answer exam questions on these issues I restrict myself to the mainstream interpretation. – John Rennie Jul 25 '15 at 6:01
• As I said on the new question, there are two interpretations. Neither is my own. When I'm answering questions for people, I don't try to portray one interpretation as the mainstream/only interpretation. Especially when it demands elephants in two places at once and a trip to the end of time and back: "In other words, the object goes infinitely far into the 'future' (of coordinate time), and then infinitely far back to the 'present'..." – John Duffield Jul 25 '15 at 6:29