General relativity is an obvious candidate. While special relativity was hanging in the air, and so was quantum mechanics, there was no urgency to improve on the Newtonian gravity at the time. There were a few small discrepancies, like the perihelion of Mercury, but not until the discovery of expanding universe a decade later it was obvious that a new theory was needed.
Yes, Hilbert formulated the equations (or at least the Hilbert action from which the Einstein field equations follow) at about the same time, a brilliant mathematician that he was, he only needed a few hints and he was familiar with Riemann’s differential geometry. The idea that differential geometry could be useful for the description of gravity as a field had been known since at least 1913, after Grossmann, Einstein’s classmate with whom Einstein had been collaborating on and off for a few years prior, since maybe 1907, published his paper on the topic. I don’t know the full history, but I was under the impression that Einstein was the main driving force behind trying to come up with incorporating Lorentz invariance into a new theory of gravity.
General relativity is an obvious candidate. While special relativity was hanging in the air, and so was quantum mechanics, there was no urgency to improve on the Newtonian gravity at the time. There were a few small discrepancies, like the perihelion of Mercury, but not until the discovery of expanding universe a decade later it was obvious that a new theory was needed.
Actually, general relativity seems to have been discovered by Hilbert at almost exactly the same time that Einstein did.
https://en.wikipedia.org/wiki/Relativity_priority_dispute#General_relativity_2
Yes, Hilbert formulated the equations (or at least the Hilbert action from which the Einstein field equations follow) at about the same time, a brilliant mathematician that he was, he only needed a few hints and he was familiar with Riemann’s differential geometry. The idea that differential geometry could be useful for the description of gravity as a field had been known since at least 1913, after Grossmann, Einstein’s classmate with whom Einstein had been collaborating on and off for a few years prior, since maybe 1907, published his paper on the topic. I don’t know the full history, but I was under the impression that Einstein was the main driving force behind trying to come up with incorporating Lorentz invariance into a new theory of gravity.