Could a super-advanced civilization live inside the acretion disk, the super-dense area around the black hole at the center of a galaxy? Author Mike Brotherton has played with this idea, and a couple of scientific papers say it's possible.
Brotherton, whose book Spider Star has creatures living in an accretion disk, points to a couple papers from the 1990s which say that it's possible that civilizations really could develop in that environment. One paper, "Accretion disk civilization 1: Habitable zone around accretion disks at galactic nuclei" by J. Fukue et al., notes that the density of stars and planets in the accretion disk is expected to be high, and wonders what sort of planets might develop there. Fukue's second paper, "Accretion disk civilization 2: From sunhook to photon floater," gets even more speculative, talking about civilizations that could harness the energy of an accretion disk using a "photon floater":
An accretion disk surrounding a supermassive black hole at the active galactic nuclei radiates tremendous energy. In order to utilize energy of the accretion disk system, the author investigates the configuration and stability of a floating platform - photon floater - above the accretion disk, which is supported by the radiation pressure of the disk radiation. In the case of the far-floater, which is located far from the disk, there exists a critical floating angle, where the gravitational force of the central black hole is balanced with radiation pressure. In the case of the near-floater, which is located very close to the disk, there exists a critical floating height, where the gravity is balanced with radiation. It is demonstrated that this floating height is dynamical stable. Finally, in the case of the axis-floater, which is located on the axis of the disk, the photon floater is unstable.
Accretion disk image from Science Clarified.