Hi Jeff, welcome to Hypography.
You can't tell the difference gravitationally between a point mass (a singularity in this case) and a spherically symmetric ball from a point outside the ball. This is true not only in Schwarzschild's metric, but GR in general. It's called
Birkhoff's theorem. So, from outside a black hole (assuming the mass is spherically symmetric) it's impossible to determine if there is a singularity versus some lower density configuration of the matter.
Schwarzchild's metric does not predict a singularity. Because the metric is static (it only works for observers who are not moving) it breaks down at the event horizon—the point where things can no longer be static. It's possible to change up the metric a bit and describe the interior of the horizon which is done with
Kruskal–Szekeres coordinates which then show that inside the horizon all future paths lead to a true singularity (rather than the coordinate singularity in Schwarzchild's metric).
Quote:
Originally Posted by Jeffocal
The surface of collapsing star from the view point of an observer who is at the center of the collapse would look according to the field equations developed by Einstein as if the shrinkage slowed to a crawl as the star near its critical circumference because of the increasing strength of the gravitation field at the surface of the star relative to it's center. The smaller the star gets the more slowly it appears to collapse because the gravitational field at its surface increases until time becomes frozen at the critical circumference.
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No, the field is strongest (greatest gravitational potential) at the center of the mass. Gravitational time dilation is proportional to gravitational potential where potential is taken to be positive, greatest at the center of the object, and decreases to zero at infinity. With smaller potential comes faster clocks. You can use the following where U is potential:
So clocks will tick faster on the surface of the collapsing star as considered from the center.
There's a good page on this topic (the geometry inside a black hole) here:
Schwarzschild Geometry
~modest
