How is singularity formed inside a black hole?

[yinfudan]

Wikipedia and some other web sites mention that: At the center of a black hole lies the singularity, where matter is crushed to infinite density, the pull of gravity is infinitely strong, and spacetime has infinite curvature. This means that a black hole's mass becomes entirely compressed into a region with zero volume. This zero-volume, infinitely dense region at the center of a black hole is called a gravitational singularity.

My question is, though it is true that the center of a black hole has an even higher density than other region inside the black hole, it does not necessarily mean that it must be a singularity, with infinite density and zero-volumn. I think the total amount of mass inside a black hole is finite, the volume of the center region is also finite, so the density is also finite, even though it can be arbitrarily high.

Another question is if singularity does exist in the center of a black hole, how is it formed? Is it formed gradually over time as mass moves closer and closer to the center, or is it formed instantly as soon as the black hole is formed?

Thanks!

 

[A-wal]

The black hole is a consequence of the singularity. It's the only thing capable of enough gravity to trap light. Singularities have 0 volume so any mass means it has infinite density. Black holes can be very small and have low masses but they still have very strong gravity, just over a smaller distance. A black hole is what happens when there gravity but nothing to provide a resisting force against it.

 

[Dale]

Another question is if singularity does exist in the center of a black hole, how is it formed?

The short answer is that we don't know. This is one of the reasons for all of the work on developing a theory of quantum gravity.

 

[yinfudan]

The black hole is a consequence of the singularity. It's the only thing capable of enough gravity to trap light. Singularities have 0 volume so any mass means it has infinite density. Black holes can be very small and have low masses but they still have very strong gravity, just over a smaller distance. A black hole is what happens when there gravity but nothing to provide a resisting force against it.

Wikipedia does not imply the black hole is a consequence of the singularity. It seems that no matter in Newtonian gravity or general relativity, as long as the mass is concentrated in the Schwarzschild radius, it forms a black hole that light within the range of Schwarzschild radius cannot escape. It does not necessarily mean the mass has to be concentrated in a zero-volume point or ring (the singularity).

Could you please explain in more details?

 

[Al68]

Wikipedia does not imply the black hole is a consequence of the singularity. It seems that no matter in Newtonian gravity or general relativity, as long as the mass is concentrated in the Schwarzschild radius, it forms a black hole that light within the range of Schwarzschild radius cannot escape. It does not necessarily mean the mass has to be concentrated in a zero-volume point or ring (the singularity).

Could you please explain in more details?

A singularity is just a mathematical concept, we don't know what is actually happening there locally. The volume the mass "inhabits" is mathematically zero in an external reference frame, but that's not a "local" description. For all we know, there's a whole other universe "inside" every black hole.

 

[Hurkyl]

Differential geometry, the mathematics upon which GR is based, does not forbid "singularities" or other sorts of holes from appearing anywhere at all.

For example, the Einstein Field Equations are 100% consistent with the hypothesis that the moon doesn't exist at all. Instead the universe has an "edge" beyond which nothing exists, and energy is emitted from this edge that gives the appearance of a moon.

Obviously, this is an unappealing state of affairs for the mathematical theory -- so we would like to impose another condition on GR that the edges of the universe (if any) cannot be reached in finite time.

(Note that infinite universes still have "edges" -- consider the Euclidean plane as a simple case. It has an edge "at infinity". This is easy to see using the coordinate system (u,v) defined away from the origin in terms of polar coordates by (u,v)=(1/r, theta): the edge "at infinity" under these coordinates is the boundary at u=0. However, such an edge is infinitely far away)

Unfortunately, this condition is generally impossible to impose -- there is a mathematical theorem that if the universe obeys the Einstein Field Equations, and there is ever a "sufficiently dense" region in space-time, then the universe must have an edge that can be reached in finite time.