Oz knocked on the Wizard's door.
"Come in," said the Wiz gruffly. Oz opened the door. Not looking up, G. Wiz asked "So, have you finished the test yet?"
"I don't know!" said Oz, his voice tinged with desperation. He hadn't slept in days.
He stepped in hesitantly. "Okay, I took your hint about dust. We have a little ball of coffee grains. Naturally, being massive, they come together. However, being pointlike, they can get as close together as they like. Now
d2V/dt2 = - (1/2)(E+3P) V
So as V gets smaller, d2V/dt2 gets ever larger since both E and P are positive, so the volume should tend to zero. The density will thus tend to infinity. I guess this might (just) be called a singularity. Certainly the curvature gets to be infinite which is good enough for me."
Oz sighed, "Personally I find this too glib and too simplistic."
G. Wiz turned around and burst out, "However, it's exactly along the lines I wanted!!!! I wanted something glib, simplistic, yet correct."
"So, keeping in mind this stuff, tell me what you can about *curvature singularities*... places where the Riemann curvature blows up. Also, how are your coffee grounds moving... are they perchance following geodesics? (I guess so, since you're using the formula that applies then.) What can you say about the more realistic case where, after they get close enough together, they "bump into each other". Doesn't this keep the black hole from forming?"
"Hmm," said Oz. " See! I was right! It *was* too glib and simplistic. At least I got something right, even if it's nothing to do with the question. You're right, I was using the formula that applied to geodesics, but in a star, say, the gas doesn't just fall in to the center along geodesics. So what happens then?" He sighed again, wiping a tear of frustration from his eye. Somewhat dazed, he walked out of the Wizard's room, not even remembering to shut the door.
The Wiz shook his head and returned to his work. "He's getting close, but he doesn't seem to know it... or even believe it when I tell him so," he muttered.