A black star was a star made of quasi-baryonic dark matter. Since it was only partially real it could become more massive than a black hole, without actually collapsing out of real-space. Moreover, such a star didn't give out any energy signature, which made them almost impossible to detect, and its semi-tachyonic nature made it a danger to the temporal vortex as well. (PROSE: Sanctuary)

During the Sontaran invasion of Gallifrey, Sontaran commander Stor ordered Castellan Kelner to drive the Fourth Doctor's TARDIS, by then President-elect, into a black star, in vain. (TV: The Invasion of Time)

The Seventh Doctor and Benny used the Jade Pagoda to escape a black star. (PROSE: Sanctuary)

In the Wrarth Galaxy, there was a black star known as Black Sun; exposure to a concentrated burst of its radiation was able to temporarily render humans violent. (COMIC: Doctor Who and the Star Beast, AUDIO: The Ratings War) The Order of the Black Sun was a time-active faction at war with the Time Lords. (COMIC: 4-D War et al.)

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