Can an observer catch the infalling matter surface in a collapsing black hole?

[pervect]

I've been reviewing what I could find about the current knowledge of what it would be like to fall into a black hole, and I think I'm beginning to get a
picture. Some of the URL's I've visited are

http://math.ucr.edu/home/baez/PUB/generichole
http://lanl.arxiv.org/abs/gr-qc/9902008
http://casa.colorado.edu/~ajsh/schwp.html
http://www.gothosenterprises.com/black_holes/inside_black_holes.html
http://nrumiano.free.fr/Estars/int_bh.html

Plus my textbooks, Wald, "General Relativity" pg 156

Here's what I'm getting - corrections would be welcome

The static Schwarzschild solution has two separate flat space-time regions, joined by a non-traversible wormhole.

If the singularity was caused by an actual collapsing shell of matter, but the idealization that the collapse is spherically symmetrical is made, the situation will be different. The collapsing matter surface itself will block any access to the alternate flat space-time regions (Wald). I believe that this implies that the matter surface will also block access to the singularity (?). In other words, the way I'm reading this, because of the infinite time dilation near the center of a black hole, a sufficiently determined observer who accelerates hard enough actually can "catch up" to the infalling matter surface! (??) (Or is that better read as - must catch up to the matter surface (?)).

Life apparently gets even more interesting when the collapse is not spherically symmetrical, for instance if there is angular momentum or charge present. Here, exactly what happens is apparently still a matter of some debate. But the latest work, the second of my link collection, suggests the it appears to be generally similar to the Schwarzschild case, except for the existence of a "weak" null singularity whose physical interpretation is not fully understood at this point.

 

[R0man]

Your understanding of the current knowledge of falling into a black hole seems to be quite accurate. The links you have provided are reputable sources and cover the various aspects of black hole physics. The Schwarzschild solution does indeed have two separate flat space-time regions, and the singularity is only accessible from the inside of the black hole. This means that the collapsing matter surface will block any access to the singularity from the outside.

As you mentioned, the situation becomes more complex when the collapse is not spherically symmetrical. In this case, the presence of angular momentum or charge can affect the structure of the black hole and the behavior of matter falling into it. The existence of a "weak" null singularity is still not fully understood and is an area of ongoing research.

One correction I would make is regarding your statement about an observer being able to "catch up" to the infalling matter surface. This is not possible due to the infinite time dilation near the center of a black hole. The observer would actually experience a never-ending journey towards the event horizon, never reaching the matter surface or the singularity.

Overall, your understanding of falling into a black hole is well-informed and you have provided good sources for further exploration. Black holes are still a fascinating and mysterious area of study in physics, and there is still much to learn and understand about them.