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"I think crypto will slowly percolate its way up and people will adopt it gradually as user friendly, cheap products, become available."
- Neal Stephenson

Manmade Black Hole  
  Using the power of a hole in the continuum.  

Jack Williamson doesn't actually use the phrase "black hole", but he does use all the words, as well as the concept. As far as I know, this is a first in science fiction (or anywhere else).

Chan Derron’s brain was staggered by that machine’s immensity, and baffled by its strangeness. Against the star-shot dark of space hung two great spheres of blacker blackness. Three colossal rings, set all at right angles, bound each of them; and between them, connecting them, was a smaller cylinder of the same dully gleaming metal.

“It looks a little bit like a twenty-million ton peanut,” he muttered. “But I never saw anything so black as those great globes!”

“They are not anything,” said Stella Eleroid. “They are simply holes in the continuum of our universe. That blackness is the darkness of a lightless hyperspace.

“It is through those holes that the geodesies are refracted,” she said. “They are held open by the achronic field coils in the rings about them. There are four rings about each globe of force—the three that you see, and a fourth that has been rotated into hyper-space.

From One Against The Legion, by Jack Williamson.
Published by Astounding in 1939
Additional resources -

This is a part of the description of the geofractor, a teleportation device from this same story.

A firm mathematical model of a gravitationally collapsed object came about in the early 1920's through work by Einstein and Schwarzschild. A 1926 book by Arthur Eddington described how even light would be unable to escape from such an object.

Apparently, the phrase "black hole" seems to derive from the Black Hole of Calcutta (a famous prison), which Europeans encountered in the mid-1700's. The idea of a "dark star" was proposed in 1783 by an English country parson, John Michell. He wrote a letter to Henry Cavendish dated November 27, 1783, saying that such “dark stars” would be observable only by the impact they had on bodies revolving around them.

The modern use seems to derive from a shouted response from the audience during a lecture by John Wheeler, who wished for a more compact term than "gravitationally collapsed object".

Compare to the asymptotic drive from Imperial Earth (1976) by Arthur C. Clarke.

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Additional resources:
  More Ideas and Technology from One Against The Legion
  More Ideas and Technology by Jack Williamson
  Tech news articles related to One Against The Legion
  Tech news articles related to works by Jack Williamson

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