Not only is it possible, it’s theoretically one of the most efficient sources of energy out there.
The black hole itself, by which I mean the event horizon and everything inside, is not a great source of energy. It was a famous discovery by the late Stephen Hawking that despite their gravity, all black holes do emit a little radiation from their event horizon, but it isn’t much. In fact, the bigger the black hole, the less power you get.
But if you throw something in to the black hole, then the fun happens. Almost every black hole is spinning very fast, and this effect pulls material approaching it into what’s called an accretion disk:
While spiraling in, the matter will go faster and faster, and wrap more and more tightly, and before it completes the descent it will start feeling intense friction against itself. Basically, it will give itself a rug burn.
(We’ve only seen this effect happen with gas from stars, but I can’t think of a reason it wouldn’t happen with anything you toss in.)
All that friction turns to heat, then to radiation. This radiation takes the form of X-rays, blasting out perpendicular to the disk:
This is such an intense effect that a lot of the gas falling in will actually disappear. Mass is energy, and energy must come from somewhere. E = mc^2. In this case, a large portion of the mass directly transmutes into X-rays. The black hole is such a gluttonous eater that a lot of what it eats explodes into light before it can get it into its mouth.
This has an absolutely insane matter → energy conversion process. For reference: the only power source we currently have that directly converts matter to energy is nuclear power, which scrapes 0.1%, a mere pittance, of the mass of U235 into energy as it splits apart. The sun’s nuclear fusion is a bit more efficient, converting 0.7% of the mass of its hydrogen into various kinds of light, the other 99.3% settling into helium.
The conversion rate of accretion disk of a black hole can be up 40% .
Forty percent!
One kilogram (~2.2 pounds) of matter converted 40% of the way into energy would yield 36 petajoules, or 10 terawatt-hours. That’s enough to power the entire world for half an hour. A metric ton could power it for three weeks.
So, the potential is there. Now we just need a way to get there :-)