Black hole creation (Penrose diagrams)

1. Jul 1, 2005

lurathis

I am currently reading "Black holes, Information and the String Theory Revolution" by L. Susskind and J. Lindesay as an introduction to GR and am having some trouble with the way Penrose diagrams are fabricated to model the creation of black holes (assumed to never die).

So basically we start off with a diagram of flat Minkowski space:

http://filebox.vt.edu/users/foster/flatminkowski1.jpg

The blue line that crosses through the diagram actually covers a black line that is meant to represent the collapse of a thin spherical shell of massless matter. Thus, the only part of the diagram that is of importance is region A (since after the collapse, we no longer have flat Minkowski space.

Meanwhile, the diagram of a black hole looks like:

http://filebox.vt.edu/users/foster/schwarzblackhole1.jpg

where again, the line traversing the diagram covers the black line representing the infalling matter. Thus, the region labelled B is the only region of importance since before the collapse there was no black hole.

Everything makes sense upto this point. I also realise that to paste them together, you must 'match areas' so to speak of the 2-sphere along that line representing the infalling matter.

This final representation would then look like:

http://filebox.vt.edu/users/foster/blackholecreation1.jpg

My first question is whether original grid-lines still apply. I mean, looking up at the previous two diagrams we can match the t=0 line and we see that in the final image they don't match up. What happens here?

My second question is also related to the gridlines. This is a diagram in the book:

http://filebox.vt.edu/users/foster/creationfieldlines1.jpg

The alarming thing to me is the two things I wrote in blue ink. I really don't understand what the lines of constant radius look like any more. We have r=0 running as a horizontal line at the top, then a r=0 vertical line running on the left. Is there a smooth transition?

[Hmm... not sure how to make the images appear in the post as opposed to a link.]

Last edited by a moderator: Apr 21, 2017