Everybody as in, the leading experts in theoretical physics of the time:
"It was noted by Sir Edmund Whittaker in his 1954 book that David Hilbert had derived the theory of general relativity from an elegant variational principle almost simultaneously with Einstein's discovery of the theory.[B 1] Hilbert's derivation of the theory predated that of Einstein by five days.[B 2]"
Be careful however, as unfortunately some, for other reasons, historically tried to appropriate this work, and use to try to diminish the contributions of Einstein. Something that of course, is very much incorrect.
That equation is associated with SR, not GR. I’m not aware of anyone, aside from Einstein and the small group at Göttingen who were working with him, and a couple of his friends, such as Grossmann, who were helping him with the math, even being aware of this work on gravity. But I’m willing to learn. Please provide some names. Who were the “experts of the domain at the time”? For that matter, what is this domain?
The equation is not more associated with SR or GR, more than its historical context where it was derived from. Its just a principle of physics SR, GR or any
other theory.
Who are the people? The Berlin Group, David Hilbert, Carl F. Gauss, Bernhard Riemann, Ernst Mach,Henri Poincaré, Hendrik Lorentz. The domain are the studies on the understanding the most basic fundamentals of physics derived from the analysis of electromagentism that most leading physicists of the time were busy with. Although Hilbert and Poincare are monsters of pure mathematics they were just doing physics by the side.
Looking at the biography of Hilbert, it starts to look like almost obvious what happened. In no way it diminishes the stature of Einstein to recognize it.
Hilbert was a monster:-) Hilbert did invariant theory, calculus of variations, commutative algebra, algebraic number theory, geometry, spectral theory of operators and its application to integral equations, mathematical physics.
Einstein by the contrary, always needed help with Mathematics, since
the times at University. That was how he met his first wife...
Hilbert was following the work of Einstein but this latest one was struggling to make any progress for years. In the summer 1915, Hilbert's was interested in general relativity, and he invited Einstein to Göttingen to deliver a week of lectures on the subject.
Suddenly within a few weeks, Einstein comes up with his Field equations while Hilbert follows with his foundations of physics. The fact that Hilbert fully credited Einstein as the originator of the theory, and did not engage in any public priority dispute is pretty clear was as a statement to the
previous work Einstein did for years. With the collaboration and common work that happened its pretty clear, Einstein did not have the mathematical prowess and skill, to come up with those sudden breakthroughs...
He had even better than mathematical prowess: an intuition and creativity. Einstein's thought experiments were what led him to the discovery. What's the difference between someone with superior raw mathematical talent and strong mathematical talent plus creative intuition? I would argue, in particular with regards to physics, it makes all the difference.
"...a paradox upon which I had already hit at the age of sixteen: If I pursue a beam of light with the velocity c (velocity of light in a vacuum), I should observe such a beam of light as an electromagnetic field at rest though spatially oscillating. There seems to be no such thing, however, neither on the basis of experience nor according to Maxwell's equations. From the very beginning it appeared to me intuitively clear that, judged from the standpoint of such an observer, everything would have to happen according to the same laws as for an observer who, relative to the earth, was at rest. For how should the first observer know or be able to determine, that he is in a state of fast uniform motion? One sees in this paradox the germ of the special relativity theory is already contained.[p 1]: 52–53 "
> Suddenly within a few weeks, Einstein comes up with his Field equations
It wasn't a few weeks, it was months. Einstein visited Hilbert in June/July 1915. He didn't publish his field equation until November 1915 (and even then it took him several tries before he got the final one).
This is sort of a myth. Einstein was a poor mathematician in comparison with Hilbert, but that goes for most of us. He was fairly strong by the standards of the era.
