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.