This is from Jagdish Mehra and Helmut Rechenberg's monumental "The Historical Development of Quantum Mechanics, Vol. 6, Part 2". With Chandrasekhar's facility with astrophysics and von Neumann's with mathematics, there is little doubt in my mind that they would have succeeded.
As it happened, it was Oppenheimer and his student Hartland Snyder who wrote the decisive paper describing black holes in 1939.
The timing was bad, though; on the same day that the paper came out in the Physical Review, Germany attacked Poland and started World War 2. Far more consequential was another paper published on the same day in the same issue - John Wheeler and Niels Bohr's liquid drop model of nuclear fission.
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