# Review article on astrophysical collapse to a black hole?

Staff Emeritus
Gold Member

## Main Question or Discussion Point

Does anyone know of a review article on astrophysical collapse to a black hole?

There are several statements I've picked up from WP that either surprise me or that I'm not sure I understand.

This Penrose diagram http://en.wikipedia.org/wiki/File:PENROSE2.PNG shows the singularity as being initially coincident with the horizon at what looks like finite r, which seems odd to me. I would have naively expected it to form at r=0, but I guess even in the Schwarzschild metric, that isn't really true; it's spacelike, not timelike, so it doesn't make sense to refer to it as having a definite position.

The diagram also shows the singularity as being timelike initially before it eventually settles down and becomes spacelike. I guess this is the only way to connect the event of formation to the eventual spacelike world-line of the Schwarzschild-like singularity.

This WP article http://en.wikipedia.org/wiki/Apparent_horizon says that an event horizon forms before a trapped null surface. (The statement is referenced to Hawking and Ellis, without a page number.) I guess the Penrose singularity theorem only guarantees that a spacetime that contains a trapped null surface must also contain at least one black hole singularity, but I'd been imagining that the trapped null surface would come first. I wonder where on the Penrose diagram the "apparent horizon" (boundary of the union of all trapped null surfaces) would lie.

## Answers and Replies

Related Special and General Relativity News on Phys.org
PeterDonis
Mentor
2019 Award
This Penrose diagram http://en.wikipedia.org/wiki/File:PENROSE2.PNG shows the singularity as being initially coincident with the horizon at what looks like finite r, which seems odd to me.
I'm not sure the diagram is really intended to show that. The worldline of the surface of the collapsing star is not well distinguished from the curve describing the singularity. It is Wikipedia, after all. :uhh:

Andrew Hamilton has some much better diagrams here:

Staff Emeritus
Gold Member
Depending on what aspect of collapse you are interested in, the references vary. This is one starting point. You may find more stuff of interest over there.

If you have something more specific in mind (analytical/numerical analysis of general/critical/simple collapse), I may be able to point at more specific reviews.

Staff Emeritus
Gold Member
Thanks, Sourabh, that's cool! I'm basically trying to understand the issues about Penrose diagrams described in #1 and #3, e.g., the apparent contradiction between the different versions of the Penrose diagram.

pervect
Staff Emeritus
The Penrose diagram of a collapsing black hole is most likelly going to be considerably different from the penrose diagram of a Kerr black hole. See for instance http://arxiv.org/pdf/1010.1269.pdf "The interior structure of rotating black holes 1. Concise derivation".

The Kerr geometry, and more generally the Kerr-Newman geometry, has two inner horizons that are gateways to regions of unpredictability, signalled by the presence of timelike singularities. In 1968, Penrose [5] pointed out that an observer passing through the outgoing inner horizon (the Cauchy horizon) of a spherical charged black hole would see the outside Universe infinitely blueshifted, and he suggested that the infinite blueshift would destabilize the inner horizon. The infinite blueshift is plain from the Penrose diagram, Figure 1, which shows that a person passing through the outgoing inner horizon sees the entire future of the outside Universe go by in a finite time.
Perturbation theory, much of it expounded in Chandrasekhar’s (1983) monograph [6], confirmed that waves from the outside Universe would amplify to a diverging energy density on the outgoing inner horizon of a spherical charged black hole. The result was widely interpreted as indicating the instability of the inner horizon.
It's impressive that we now (apparently - I need to read this more carefullly myself) have an actual metric to describe for rotating collapse. When I was attempting to read previously about the expected issues, for actual collapse, some of which have been dubbed "mass inflation" by various authors (Penrose and later Hamilton), the lack of an actual metric always made it difficult for me to understand what was being said.

But there's still an important assumption being made for mathematical tractability, which is axis symmetry. Unfortunately, it's rather likely that this assumption is going to fail in the interior region. I.e. if you have a collapsing cloud of dust, and it has density fluctuations, you're going to see the density fluctuations grow more pronounced as the dust collapses, spoiling the axis symmetry even for an initially fairly homogeneous dust.

Anyway, that's my take on the current state of the art of this fascinating and tricky subject.

@bcrowell - I cannot say anything about the WP conformal diagram (it looks flat out wrong at first glance, but I'll get back to you). As for the diagram in #3, it is common practice to draw the center as a vertical line (since the center is supposed to be timelike). But if you actually perform a transformation to Kruskal Penrose coordinates, the resulting causal structure, at least for certain dust collapse, is closest to the one in the link in #2.
I think that depending on the exact conformal transformation, all these diagrams can represent the same model of collapse.

PS - It has been six months This reply might be outdated. Please share any new insights you may have!

@atyy Thanks for that Rezzolla article.