Star Trek 'Tomorrow is Yesterday' (1967)
While en route to Starbase Nine, the Enterprise flies too close to a "black star," which produces no energy but produces an immense gravitational pull. When the ship breaks away, it creates a timewarp that hurls the Enterprise back to the late 1960s.
At the time this episode was recorded, astronomers had not yet started using the term "black hole," to the writer's description of a "black star" was accurate â€" it's not something you want to wander close to, even in a powerful starship.
The idea of creating a timewarp when you pull away from the black star doesn't work, though -- at least not as a way to travel backward in time. However, a ship that passed close enough to a black hole to require warp power to escape would experience "time dilation," an effect in which time seems to pass more slowly on the ship as seen by an outside observer. So when the Enterprise escaped the black hole's gravity, it would discover that its chronometers were behind those of other ships and starbases. So in that respect, at least, the valiant crew would have traveled "back" in time.
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Other black hole references in pop culture...