Would gravitational time dilation prevent Singularity in a black hole?

[BenjaminShaw]

In the current mainstream theory of black holes, there exists a singularity of infinite density. However, it seems to me that matter actually could not compress tightly enough to reach this point. As matter coalesces in a black hole, space-time would increasingly curve. As the density approaches infinite, so would the curvature of surrounding space-time. This in turn would mean that time becomes almost infinitely dilated, all but stopping the flow of events. Therefore, there would not be enough time for matter to move close enough together to actually reach infinite density. If I am correct on this, it would seem to vindicate Einstein's belief that a singularity should not exist in nature.

Is there a major flaw in my understanding of gravitational time dilation or limits at infinity, or might this actually be a reasonable extension of Relativity that would eliminate one of the most mathematically objectionable aspects of black holes? This seems simple and straightforward enough that I must be missing something major.

 

[Drakkith]

Do a search here on PF for this. I swear I just saw an identical post recently.

 

[bcrowell]

According to GR, in a Schwarzschild spacetime, infalling matter reaches the singularity in finite proper time. In fact, the Penrose singularity theorem proves that under certain conditions, a singularity must result.

If you look at other theories instead of GR, you can get a different answer. For an example, see http://arxiv.org/abs/0902.0346 . There is a good popularized version in Scientific American, Oct. 2009, if you can find it at a library.