I've always been curious about how rigorous are the Casimir force measurements carried out, because a couple of years ago I read some news about people inventing perpetual motion machine which turned out to be draining power from environmental EM noises, say, radio station, wifi, 3G/4G that keep...
Lucky for you, cause I've seen people calling it paraboloid surface or something in several literatures.
In another book, the author even explains that the paraboloid is a parabola rotating around its axis of symmetry (which is generally correct but not in this case), which made me feel WTF for...
Alright, then we do agree that this "Flamm's paraboloid" is NOT what mathematicians defined as "paraboloid", that whenever we mention it, we should call it "Flamm's paraboloid" as a whole, right?
I think that it's like we don't rotate an ellipse around an arbitrary inclined axis and call that an...
But then the Flamm's paraboloid looks nothing like a well-defined paraboloid!?
Can we just rotate a parabola around an arbitrary line and call that a paraboloid!?
But if we rotate it around the ``correct'' axis to get the real paraboloid of revolution: https://en.wikipedia.org/wiki/Paraboloid
Now it looks nothing like the ``Flamm's paraboloid'' (or, Einstein-Rosen bridge)...
The shape of the Einstein-Rosen bridge is often visualized/modelized with the Flamm's paraboloid, and many other references have also stated clearly that it's a "surface of revolution of a parabola".
But as far as I can see, when we rotate the parabola w^2 = 8M(r-2M) (in natural units c=G=1)...