Difference betwen space-like and time-like singularities

[Afonso Campos]

See the Wikipedia article on Penrose-Hawking singularity theorems: https://en.wikipedia.org/wiki/Penrose–Hawking_singularity_theorems.

It says that

A singularity in solutions of the Einstein field equations is one of two things:

1. a situation where matter is forced to be compressed to a point (a space-like singularity)

2. a situation where certain light rays come from a region with infinite curvature (a time-like singularity)

If matter is forced to be compressed to a point, why is this called a space-like singularity?

If certain light rays come from a region with infinite curvature, why is this called a time-like singularity?

 

[PeterDonis]

Heuristically, a spacelike singularity is like a moment of time, and a timelike singularity is like a place in space. So if matter is compressed to a point (a better term would be "energy density increasing without bound"), this happens at some moment of time, hence the singularity is spacelike. But if light rays are coming from somewhere with infinite curvature (a better term would be "spacetime curvature increasing without bound"), that somewhere is a place in space, hence the singularity is timelike.

 

[Afonso Campos]

Heuristically, a spacelike singularity is like a moment of time, and a timelike singularity is like a place in space.

Oh, so, is this simply a terminology with no physical meaning? Surely, there must be a reason why singularities that are like a moment in time are called spacelike, and singularities that are like a place in space are called timelike!

But if light rays are coming from somewhere with infinite curvature (a better term would be "spacetime curvature increasing without bound")

How can it be possible for light rays to escape from a singularity?

 

[martinbn]

Oh, so, is this simply a terminology with no physical meaning? Surely, there must be a reason why singularities that are like a moment in time are called spacelike, and singularities that are like a place in space are called timelike!

Perhaps you need first to understand what spacelike and timelike mean. These term have a specific technical meaning in relativity. The words in English may sound vague but here they have a precise meaning.

How can it be possible for light rays to escape from a singularity?

And why not? It simply means that the null curves, which are the world lines of the light, are past incomplete (and in PeterDonis' example there is a curvature blow up).

 

[PeterDonis]

Oh, so, is this simply a terminology with no physical meaning?

Not at all. As martinbn said, "spacelike" and "timelike" have a very precise meaning in relativity. Any textbook will explain them.

How can it be possible for light rays to escape from a singularity?

Because this type of singularity is like a point in space, from which anything could come. Since the laws of GR break down at the singularity, we have no way of predicting what could or could not come out of it.