Can there be habitable exoplanets orbiting a black hole if the black hole has an accretion disk?
The 2014 sci-fi film Interstellar features a team of astronauts exploring several planets orbiting a supermassive black hole to assess their suitability for human life. Could such planets exist somewhere out there? We know that the universe is full to bursting with planets, but we yet don't know of any that orbit a black hole (let alone of the wormhole we'd need to travel there). Still, it's interesting to think about the factors that could affect whether life as we know it could exist on such worlds.
Black holes, as the name suggests, do not emit energy in the form of light on their own (okay, maybe some Hawking radiation, but that's a tiny amount). As such, a black hole on its own would not be able to give light or heat to sustain life on nearby planets. Fortunately for our hypothetical world, many black holes have an accretion disk -- a thin, dense, disk-like stream of matter being "funneled" by gravity toward the black hole's event horizon. As matter in the disk falls inward, it heats up and begins to glow brightly, allowing us Earthlings to view them from afar and, potentially, warming the surface of a nearby planet.
It turns out that the amount of energy emitted as light by a black hole's accretion disk can related to the black hole's mass with reasonable accuracy; this estimate, called the Eddington limit, has been successfully used to describe the amount of energy emitted by supermassive black holes in galactic nuclei. So, for argument's sake, let's imagine our planet is orbiting a black hole with 10 million solar masses with an accretion disk: the Eddington limit tells us that the energy output (or luminosity) of the disk is about 300 billion times the energy output of the Sun!
Given this huge amount of light and heat, at what distance from the black hole would an orbiting planet have the right temperature to support human life? That is, where is the black hole's "habitable zone"? It turns out that an Earth-like planet would have to be extremely far away: about 550,000 farther than the distance between Earth and the Sun, over eight and a half light years! A "year" on such a world, the time to complete a single orbit, would be 130,000 Earth-years long! (If you thought 2020 would never end for us...)
Even if temperatures are right for liquid water to be present on the surface, there's no guarantee that enough water would be there. Another challenge for life on our planet is that a supermassive black hole emits light over a different range of frequencies -- "colors" of light -- than the Sun. Whereas the Sun emits mostly visible and infrared light, an accreting black hole would emit a large amount of its energy as ultraviolet light, X-rays, and gamma-rays. These energetic photons can damage or kill living cells; if you want to live on a planet near a black hole, you'd better stock up on sunblock!
There are many other factors that affect a planet's habitability, so it's not difficult to say with certainty where we might be able to fine life. It's a big universe, and it's good to keep an open mind to the possibilities.