"Today it is well known that one cannot construct a single coordinate system to describe plane gravitational waves without encountering a singularity somewhere in spacetime"
Yeah, I mean, who doesn't know that. That's like middle school stuff right there.
It's probably worth clarifying this, the basic idea is relatively simple (if you know calculus).
Consider the curve x=y^2. This curve is just a parabola, rotated 90 degrees clockwise, and is completely smooth. No angles, no jumps, no nothing.
You can parameterize this curve in the following way:
(x(t),y(t))=(t, sqrt(t))
This coordinate system is singular at t=0: sqrt(t) has no derivative there. But the curve itself is smooth. This is the type of singularity Einstein et al found.
In this simple example the singularity can be removed with the parameterization (t^2,t).
A standard result of GR (I think Tipler proved it) says that gravitational waves always have this type of singularity. But it's really not a physical singularity, since you can change it's location by changing coordinates.
"It is well known" is shorthand for "I don't want to bother figuring out the correct original reference for it", not "the average layperson knows this".
no, it is rather a shorthand for "I cannot explain the basic concept behind it clearly in a few words, because I fail to fully understand it"
Anyway, this paper publishing business has become an industry, which has little to do with exposing/exchanging ideas/thoughts on a given topic. It has become an industry for justifying applications for grants, as most people rather game the system then be left without a paycheck. See the story behind the Bose-Einstein condensate: Einstein had hardly anything to do with it -- except to open the door to the publisher (who btw has also nothing to do with it, still owning the copyright to Bose's work)
Yeah, I mean, who doesn't know that. That's like middle school stuff right there.