I'm sorry that you feel that way, but the geometry of Einstein manifolds involves more than just Schwarzschild coordinates ( which are arbitrary and not in any way privileged ). As such, it is important to go beyond the description in a specific set of coordinates and understand the

**geometry** of the space-time in question, as opposed to just an arbitrary coordinate choice. That is what I am attempting to do - we all know that Schwarzschild coordinates become singular at the event horizon, but that singularity is a feature of the

**coordinate system**, not the physics of the space-time itself; choose a different set of coordinates for the same space-time, and the singularity at the horizon vanishes, i.e. Kruskal-Szekeres, Gullstrand-Painleve, Novikov, Eddington-Finkelstein etc etc. The only singularity that is physical is at r=0, because

**all** coordinate systems are undefined there. To distinguish between coordinate singularities and physical singularities, one usually employs the various invariants of the curvature tensor, such as the Kretschmann scalar which I quoted.

Basically, I am attempting to point out that coordinate systems are arbitrary choices, but the underlying geometry of the space-time is not; we should hence focus on quantities that do not depend on the choice of coordinate system ( i.e. quantities on which everyone agrees ) when analysing this situation.

Does that make sense ?