Star Trek: Voyager, 'Parallax' (1995)
Voyager finds itself trapped inside the event horizon of a "quantum singularity" -- in other words, a black hole. After experiencing odd optical effects, such as seeing their own ship in the viewscreen, the crew finds a way to "crack" the event horizon and escape.
It would be difficult to find yourself inside a black hole without realizing that you had entered it. The black hole's effects on the space around it would create distortions that would be clearly visible.
Once inside the black hole, it might be possible to continue to orbit its center without being torn apart, but only if the black hole were extremely massive. In a stellar-mass black hole, the difference in gravity from the event horizon to the singularity at its center is so great that anything that enters the black hole is instantly ripped apart. A supermassive black hole, however, is so large that the gravity gradient is small, allowing an object to hold itself together -- at least for a while.
As for cracking the event horizon and escaping? Forget it. The horizon is not a solid surface. Instead, it is the distance from the center of the black hole at which the speed needed to escape the black hole's grip is greater than the speed of light. Since the horizon is not a physical object, there is nothing to crack -- and no way to escape.
Of course, if you have engines that can also warp space just as a black hole's gravity does, perhaps there's a way out. But you need a Starfleet engineer to work it out -- not to mention a few shortcuts around the known laws of physics.
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.
Doctor Who, 'The Three Doctors' (1973)
The Time Lords are in trouble. A black hole is draining the energy of their home planet, Gallifrey. To save themselves, they dispatch all three incarnations of their most famous renegade, the Doctor. He and his companions are drawn into the black hole, where they meet what is left of Omega, a founder of the Time Lords, who used the black hole to create the ability to travel through time. Now he threatens to use the black hole to destroy the universe if the Doctor refuses to change places with him.
Traveling through a black hole is a popular concept in science fiction, but it just doesn't work. Anything that enters a stellar-mass black hole is first ripped apart by the tidal forces, then its atoms are crushed into a new form of existence as they reach the overpowering gravitational field at the center. Even a clever engineer like Omega, who gave the Time Lords the power of time travel, could not set up a cozy nook inside the black hole's event horizon.
Doctor Who, 'Impossible Planet' (2006)
The Doctor's time machine, the TARDIS, materializes on a planet that is orbiting near the inner edge of an accretion disk around a stellar-mass black hole. A team of researchers is studying the planet, which produces an odd gravity field that keeps it intact against the tidal effects of the black hole's gravity. Anything that leaves the confines of the research station, though, is slowly pulled off the planet's surface and into the black hole.
A planet or any other object with a strong gravitational field orbiting inside a black hole's accretion disk would not last for long. The combined gravity of the object and the black hole would cause them to whirl around each other faster and faster, spiraling inward as they did so. The stress would easily destroy a rocky body like a planet, leaving only a pile of rubble to heat up and vaporize before it fell into the black hole.
And any planet close enough for the black hole's gravity to pull objects off of its surface would itself be ripped apart in a hurry. Staying inside a research base would afford no protection at all.
Stargate: SG-1, 'A Matter of Time' (1998)
"Captain, relativity gives me a headache." - Gen. Hammond, Stargate Command
SG-10, a team of explorers from Earth, is studying a planet that orbits a star in a binary system when the star's companion suddenly implodes to form a black hole. As the black hole's gravity pulls the planet toward it, the team tries to escape through the Stargate, a device that creates an artificial wormhole that connects to Earth. Time dilation effects slow SG-10's movements relative to Earth, however, making escape impossible. Worse, the black hole's gravitational field "traps" one end of the wormhole, making it impossible to disengage the Stargate and threatening the destruction of Earth.
This episode includes some excellent animation of a black hole accreting matter from its bloated companion star, as well as spot-on explanations of time dilation, tidal gravity, and other effects of a black hole.
There are a few goofs, though.
First, the episode shows a small star simply collapsing to form a black hole, which cannot happen. A black hole forms from the collapse of the core of a massive star, which is accompanied by the destruction of the star's outer layers.
And second, after a star collapses to form a black hole, its gravitational effect over a long distance doesn't get stronger. If our Sun collapsed, for example, Earth would feel no additional tug toward it. Since the planet the team was exploring was far away from the original star, it would have felt no extra tug after the star collapsed to form the black hole.