Why isn't general relativity the obvious thing to try after special relativity?
To preface my question, I ask this as a mathematics student, so I don't have a very good sense of how physicists think.
Here is the historical context I'm imagining (in particular taking into account the development of differential geometry in the 19th century):
Classical mechanics is about Lagrangians of matter fields on $\mathbb{R}^3$ (with the flat metric)
Sometime in the 1820s <PERSON> speculated about replacing the flat metric on $\mathbb{R}^3$ by one with non-vanishing curvature
Special relativity is about Lagrangians of matter fields on $\mathbb{R}^{3,1}$ (with the flat metric). I'm taking this jump for granted since as I understand it, it was arrived at from experimental results on electromagnetism at the end of the 19th century.
Now in line with <PERSON>, it seems like it would be extremely natural to speculate about replacing the flat metric on $\mathbb{R}^{3,1}$ by one with non-vanishing curvature (and in the same spirit also considering more exotic topologies for the underlying manifold).
Given that then we would have to ask exactly which metric we are looking for, it seems natural to say that there should be a Lagrangian term corresponding to the metric. The <PERSON>-Hilbert functional is probably the simplest one to try. And so we get the <PERSON> equations.
Alternatively (as I heard from someone is the actual history) you could observe that the energy-momentum tensor is of course a 2-tensor, and so for an Euler-Lagrange equation the most natural metric-dependent expression would be $\operatorname{Ric}=T$. 651
Since $T$ is always divergence free it would be natural to replace $\operatorname{Ric}$ by $\operatorname{Ric}-\frac{1}{2}Rg$ just from taking the contracted second <PERSON> identity into account. And so again we get the <PERSON> equations.
I've often heard it said that if <PERSON> had not come up with special relativity, someone else probably would have in the next five or ten years. However if he had not come up with general relativity, it would have taken much longer to discover. Why is this? I feel that I must be missing something here. 397