Chief Justice John Marshall - CC
a truly rigid body
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 a standstill 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.
This leads to a notable effect on rotation, but before we can check this out we need to extend the reasoning to rotating (or Kerr) black holes.