Chief Justice John Marshall - CC
Truly rigid bodies
Because time stands still for a distant observer, no two points inside a black hole will ever move closer together, whatever forces are applied; and therefore a black hole must be a truly rigid body in a way that no other physical object in the universe can ever be. This is a special kind of rigidity; what is known as Born rigidity, which does not negate the effects of special relativity.With this new view, we have to consider a black hole as being a solid and totally rigid sphere. A region of space where mass is as great as it ever can be. The addition of any more mass must inevitably make the black hole larger.
Even if this seems a step too far, to those well-schooled in the existing view of a central singularity, we do not have to travel inside a black hole to make this assertion. In Schwarzschild coordinates, the time coordinate slows ultimately to zero at every point on the event horizon. Now, no two points on the event horizon can ever move relative to one another and hence the event horizon itself is a Born rigid spherical shell. I will leave it to you to puzzle out what this really means if all the mass were concentrated at a central singularity.
If you think that this result is just a peculiarity of using Schwarzschild coordinates, then see Defending the Schwarzschild singularity, which shows that this must be true in any coordinate system; coming later.