I Would it be possible for a black hole to have a "solar system"?

[BHL 20]

Was just wondering if there is anything fundamentally preventing a system of planets being in permanent orbit around a black hole, without ever spiralling in. Assuming that the black hole doesn't absorb any significant amount of additional mass. Of course I know it wouldn't provide any energy to the planets like a star does, but other than that would there be any differences?

 

[phinds]

Permanently, no because over an unimaginably long period of time, the black hole will evaporate due to Hawking Radiation. In the short term it's likely there could be stable orbits for planets, BUT ... it's hard to see how they would get into stable orbits in the first place.

 

[PeroK]

Was just wondering if there is anything fundamentally preventing a system of planets being in permanent orbit around a black hole, without ever spiralling in. Assuming that the black hole doesn't absorb any significant amount of additional mass. Of course I know it wouldn't provide any energy to the planets like a star does, but other than that would there be any differences?

They are called blanets:

https://en.m.wikipedia.org/wiki/Blanet#:~:text=A blanet is a member,like planets that orbit stars.

 

[Vanadium 50]

Why would a planet orbiting a black hole be any more prone to spiraling in than one orbiting a star?

 

[Ibix]

Was just wondering if there is anything fundamentally preventing a system of planets being in permanent orbit around a black hole, without ever spiralling in.

There are stable orbits around black holes just like anything else, so yes you can have planets. Replacing the Sun with a one solar mass black hole would not affect our orbit, although as you note it would get very cold around here quite quickly. The process of turning a star into a black hole, though, is quite violent and I'd tend to suspect that any planets around one either formed or were captured after the black hole formed.

There are a couple of notes to that. First, as @phinds notes, black holes are predicted to evaporate. But the timescale for this is many times the age of the universe, so it's not an immediate worry. Second, all orbiting bodies emit gravitational waves which sap energy and cause them to spiral in. In the case of the Earth's orbit the emission is expected to be about 100W at 10^-7Hz (undetectably tiny with almost any technology). The emission power depends strongly on the orbital radius and orbital speed, and it is this mechanism that causes very dense objects like black holes to spiral into each other - they can get very close to each other while going very fast and not disintegrate under the tidal forces, so they can emit powerful gravitational waves at high frequencies detectable to us and spiral in. But for the earth, you jumping up and down is a bigger effect.