Black Holes contort space-time around them in a curious way. Any other cosmic mass can be orbitted down to its surface, but a black hole has a minimum orbital distance that’s 3 times the radius of the Event Horison, the ‘effective surface’. Objects on circular orbits will fall in towards the black hole if they come any closer. Light itself can follow an unstable circular orbit at half the above distance. Everything falls if it gets closer, though it might escape closer approaches if it’s on a hyperbolic orbit. If not, the fall inwards will speed the mass up to high speeds. Lots of infalling mass will collide and heat up, releasing up to 5.7% of its rest mass energy. By comparison hydrogen fusion releases 0.7%, thus black holes are highly efficient energy sources in the cosmos.
With that in mind, what scale of energy production can an Industrialised Super Massive Black Hole (ISMBH) achieve? There’s a guesstimate in astronomy called the Eddington Limit, named after early 20th Century astrophysicist Arthur Eddington, which is the energy production rate at which the radiation pressure matches the gravitational attraction of the object. This can vary according to the gas in the outer layers, but for hydrogen it’s 1.26E+31 watts or 32,000 times the luminosity of the Sun. Thus a 100 million solar mass ISMBH shines with the light of 3.2 trillion Suns. By comparison our Galaxy’s stars collectively radiate about 1/100th that output.
Using the 0.057 mass-energy fraction the infall rate of gas into the ISMBH can be computed: 2.46E+23 kg/s or 3.34 Earth Moons per second.
That’s an incredible rate of consumption. Equal to 3.9 solar masses per year, which means the ISMBH can’t run at peak power for too many aeons before eating its whole Galaxy. However, because the gravitational energy released is greater than nuclear fusion for every kilogram of mass, a more sedate power production level could replace starlight for a Galaxy’s needs.
The bare bones description of an ISMBH was discussed in this paper:
Type III Dyson Sphere of Highly Advanced Civilizations around a Super Massive Black Hole
More recently a general discussion of the detectability of Dyson Spheres around Black Holes has been published:
A Dyson Sphere around a black hole
One less industrial option is using the ISMBH to illuminate planets. Sean Raymond has speculated that millions of planets could be placed in the habitable zone of an SMBH:
The Million Earth Solar System
However Civilizations may not be the only beneficiaries of ISMBH’s. Space-adapted lifeforms or more traditional lifeforms on free-floating planets may well surround the ISMBH in a Dyson Cloud:
Active Galactic Nuclei: Boon or Bane for Biota?
One of the authors has an engaging popularised discussion of the concept here: Paradise for Life by the AGN Light
Sounds like a Degenerate Era project. All that mass-energy still in the local group.