“Singularity” is episode fourteen of season one of Stargate SG-1.
SG-1 are travelling to a planet during an eclipse of the sun when it should be possible to see the accretion disk of a nearby black hole. Which sounds like a bit of a scary experience.
SG-7 went through in advance to set up a telescope. When they arrive they come across someone who appears to have been killed by a disease, and then they discover SG-7, all dead.
After going back to the SGC for decontamination, SG-1 returns to find out what happened and see if there are any survivors. Apparently the locals had a legend that with the darkness would come an apocalypse, which certainly seems to have come true.
They find a young girl who has survived, possibly because she has naqahdah in her system. And something else.
The majority of the story is about the girl, Cassandra, not the black hole, although I’m not sure I’d want to go to a planet that close to a black hole.