[sjastro]

Originally Posted by Jarvamundo

We have been through this in a prior series of discussions, where we came to a head over inverse Gaussian curvature vs the radius. "the r" in the Schwartzchild solution, which you now admit is not his actual solution?

Where do you come to this stunning conclusion???

Schwartzchild solution is based on the assumption that space-time has a spherical symmetry, so r is a radial measurement. End of argument.

I respectfully. left that discussion still uneasy with the sharp step like event horison of a SMBH. As you continue to point out... "it's the smaller black holes you need to watch out for". If you just stand back from this, it is a bit contradictory (that is without the hilberts derivation imprint).

What has Hilbert got to do with Kerr, given that Hilbert had the termerity for being dead for twenty years when Kerr came up with the metric for rotating black holes?

The discussion revolved around Kerr's metric. Nothing to do with Schwarzchild and nothing to do with Hilbert. Rotating black holes don't even have "real" singularities.
There is no contradiction.

To me it seems, still to this day, un-intuitive for a geometric model, to have a SMBH appear less dangerous than a BH. Granted this is not the basis for Crothers proof, but you just see where my curious-laymen headspace is here.

Of course you don't understand because you are mathematically illiterate.
What is unintuitive to you is straightforward to anyone who understand the maths.

It was after this I discovered the works of Stephen Crothers, so far i have not seen his hypothesis been refuted. Rather he was flown to the German Royal Society to present this, and continues to. You mention that "even an undergraduate can spot his errors".... well why would his PHD professor need to fly to London to consult his Nobel laureate peer? Surely consulting an undergraduate would've been easier?

Anyways it's all irrelevant, i'd be very interested in where you can show Crothers to be wrong, i'm sure he would too?

Let me explain to you without any mathematics.
Einstein's field equations are so difficult that it is not possible to solve from first principles like an algebraic equation or simple ordinary differential equation.
Solving Einstein's equations is done in reverse. You construct a potential solution where the mathematics of the solution are based on certain physical assumptions. You then plug the solution into the field equations to see if it works.

Schwarzchild's solution is based on this principle. One of the physical assumptions made in the Schwarzchild solution is that space-time around a body has a spherical symmetry and r is a radial distance. There is no other way to interpret r.

The other issue is the singularity. Schwarzchild's solution is an example of learning to crawl before you can walk. It represents a simple solution of a non rotating black hole. Non rotating black holes probably don't exist in nature. Rotating black holes despite your protestations do exist without being burdened with singularities.

So it is a moot point to discuss singulariities in nature as the source of the singularities, non rotating black holes probably don't exist.

Steven