As a layman, this is something I've wondered about. I understand that an object larger than around three solar masses will shrink to a black hole. That amount of mass is necessary for the force that keeps electrons in their quantum areas of probability to be overcome. So those electrons' fields collapse and they join the protons and essentially create a neutron star. How do scientists know what happens at that point? How do they know what forces allow neutrons or perhaps quarks or leptons to maintain their size and shape? How do they know that there isn't some force, presumably undiscovered, which prevents them from collapsing to zero size?

 

I think I've read that many physicists nowadays are unsure of the singularity theory, expressing the fact that nobody knows what happens under black hole conditions. Is this the kind of question that has prompted such thinking?

Singularities exist within the context of General Relativity, which is a classical theory. It is suspected that a quantum theory of gravity would be able to describe the center of a black hole without singularities, but such a theory does not currently exist. It is generally believed that there's not "really" a singularity there (in the sense that there's actually a discontinuity in an otherwise smooth spacetime), but they are predicted by the math of GR.

 

The reason we know, classically, that extremely dense objects must collapse to a singularity is due to a pressure analysis of spherical bodies. It is possible to show, with a few assumptions, that once a sphere is compressed to a radius of [math]R=9GM/4c^2[/math] that the amount of internal pressure required to resist gravitational collapse becomes infinite. (G= gravitational constant, M=mass of sphere, and c=speed of light.)

Why the belief that black holes collapse to a singularity?

they don't collapse to singularity

 

How do scientists know what happens at that point? How do they know what forces allow neutrons or perhaps quarks or leptons to maintain their size and shape? How do they know that there isn't some force, presumably undiscovered, which prevents them from collapsing to zero size?

 

 

they don't know..

As CCWilson very perceptively suggests, some force (as yet undiscovered) probably intervenes to prevent the collapse to a "singularity".

 

The idea that billions of tons of matter can collapse into some kind of "zero-point" nothingness, may simplify our maths. But I doubt it happens in reality,

The reason we know, classically, that extremely dense objects must collapse to a singularity is due to a pressure analysis of spherical bodies. It is possible to show, with a few assumptions, that once a sphere is compressed to a radius of [math]R=9GM/4c^2[/math] that the amount of internal pressure required to resist gravitational collapse becomes infinite. (G= gravitational constant, M=mass of sphere, and c=speed of light.)

Elf, this may well be beyond my mathematical abilities, but what are the necessary assumptions, and how could one be sure that compression to that degree is even possible?

Elf, this may well be beyond my mathematical abilities, but what are the necessary assumptions, and how could one be sure that compression to that degree is even possible?

 

The original derivation is here: http://journals.aps.org/pr/pdf/10.1103/PhysRev.116.1027 .

 

they don't collapse to singularity

 

they don't know..

 

 

They don't know but you do?

When you have ultra-dense material of normal matter, one of the important reason sit ceases to collapse is the Pauli exclusion principle: the electrons can't all be in the same quantum state (called a degeneracy). So there's something called degeneracy pressure, which keeps white dwarf stars from collapsing further.

 

But if you get enough mass, they do, and form neutron stars

http://en.wikipedia.org/wiki/Chandrasekhar_limit

 

Neutrons are also fermions and obey the Pauli exclusion principle, meaning the, too, will exhibit degeneracy pressure. And there is a limit to this, above which they, too, must collapse.

http://en.wikipedia.org/wiki/Tolman–Oppenheimer–Volkoff_limit

 

There's nothing known to prevent further collapse above this limit.

It is possible to show, with a few assumptions, that once a sphere is compressed to a radius of [math]R=9GM/4c^2[/math] that the amount of internal pressure required to resist gravitational collapse becomes infinite. (G= gravitational constant, M=mass of sphere, and c=speed of light.)

 

When math shows infinite, it is usually wrong.

 

They don't know but you do?

 

I maybe would agree, that in a moment of explosion each single particle of positive antimatter and negative matter reaching zero point, but not in a view that in a beginning was some small point, and something happens and its explode... NO !

( just my logic )

 

When math shows infinite, it is usually wrong.

 

That's exactly what I'm saying. It is "wrong" because we start by asking the question, "what is the internal pressure some spherical mass distribution would need to resist collapse at R<9GM/4c²." The answer we get is infinity, so that means there was a flaw in our assumptions - namely that the sphere can resist collapse. In other words: the pressure required to resist collapse is infinite, therefore it does not resist collapse.