On The Scientific Origins Of Black Holes
Every gravitating body has associated with it an escape velocity. In 1783 John Michell calculated that if a star were to shrink, its escape velocity would rise, eventually reaching the speed of light. Using Newton's The Law of Gravity and the corpuscular theory of light, he reasoned that a particle of light emitted from such a star would rise a certain distance and then fall back to the surface. Obviously such a star would be dark.
As Newton's theory of gravity was replaced by Einstein's relativity theory, the effect a star had on the light it emitted had to be recalculated. Karl Schwarzschild performed the calculations, and first described the space-time geometry around such an object. This geometry showed that if a star shrinks below the Schwarzschild radius, then light would have an infinite redshift, effectively removing all the
lights energy, again making the star dark.
However no physicists believed that such an object was physically possible and could never form naturally, in fact Einstein performed a calculation to show they were impossible. In 1935 Chandrasekhar showed that for a star greater than 1.4 solar masses, electron degeneracy pressure would not be enough to stop the star collapsing, at the time this implied that nothing would halt the collapse of the star. As this was considered impossible most physicists believed that at some point a real star would shed mass to bring it under this Chandrasekhar limit.
Zwicky hypothesised as early as early as 1933 that a star could be composed entirely of neutrons. A star so massive that its gravity overcomes the electron degeneracy pressure , forcing the electrons into the protons, converting them into neutrons. This neutron star could provide a explanation for the colossal energies released in a supernova explosion. If neutron stars existed, this would imply that there could well be another limit above 1.4 solar masses, where neutron degeneracy pressure is not enough to prevent further collapse. But nobody thought of this at first...
In 1938 J. Robert Oppenheimer and a student, Volkoff, used work by Tolman, to calculate if an upper limit for a neutron star's mass existed. They found there was a limit, and it was between half and several solar masses. No one knew if another limit existed, further preventing ultimate collapse.
The second world war intervened, but in 1956 John Archibald Wheeler considered the above work, and set out to calculate whether or not there would eventually be an ultimate collapse. One of his students calculated the final fate of all circumferences of masses, which showed finally that neutron star was the final stable state. They also showed that a star above three solar masses would be unstable as a neutron star, and would turn into.... what?
Wheeler argued that the star would radiate mass away as it collapsed through some, as yet unknown, reason. His rationale was that infinite collapse was impossible, and somehow quantum mechanics could convert the mass into radiation which could escape. (This is not entirely incorrect, see Hawking Radiation)
Oppenheimer took an opposing view; that only the theory of relativity was necessary to model the collapse, and a state if infinite density was inevitable. However this argument involved huge generalisations, and might not be true in the 'real world'.
Wheeler didn't come around to the idea until computer simulations of a collapsing star,(adapted from simulations of fusion bombs), proved that the losses due to ejection of matter, radiation etc. could not prevent the gravitational collapse. Also a paper by Finklestein helped to resolve a paradox due to relativity; once the star has collapsed to the point at which light can no longer escape, shouldn't the time dilation effect become infinite, and 'freeze' the star forever at this point? Finklestein reformulated the model of the space-time in and around the star. He created a reference frame large enough to cover the area outside of the star, and the surface of the star. This showed that, yes from an external point of view, the star would appear to 'freeze', as the photons take an infinitely long time to crawl out of the gravity well, but someone sitting on the surface of the star would not see any freezing. They would ride the collapse with no pause at all, until the singularity...
Wheeler joined other physicists, such as Roger Penrose and Landau in believing such objects were possible, even inevitable. In 1967 Wheeler found the perfect name for such an object, he termed them Black Holes . The name stuck.
Of course science is often not content to leave things alone, and as black holes do not rely on the theories of quantum mechanics, their description is not yet complete. It is even possible Einstein was right, and a black hole in it's traditional formulation can not be created from a real object, if quantum machanics are taken into account. One such description of matter stressed to such a degree is that of a 'Gravitional Condensate Star' or a 'Gravastar'.
For more info, I'd recommend the book 'Black Holes and Timewarps : Einsteins Outrageous Legacy' By Kip S. Thorne ISBN 0-33-63969-3 which I used in the writing of this article.