What do black holes spin relative to?
In other words, what is black hole spin measured in relation to?
Spinning black holes are different from non-spinning black holes. For instance, they have smaller event horizons. But what are the spins of black holes measured relative to?
Let's first look at an example with common objects.
Example
Let's say there's a disc on a table that rotates at 60 rpm. When you are standing still it spins at 60 rpm. But if you start running around it, it will move faster or slower relative to you. In this case, the disc has a ground speed, 60 rpm, because it has something to spin in relation to, in this case, the table.
Black Holes
Now, let's say that there is a spinning black hole. Because there is no control for the black hole to spin relative to, its spin must be relative to an object, for example, you. If you stand still, it spins at a constant rate. But if you start moving around the black hole in the same direction as the rotation, according to Newtonian physics, the black hole would spin at a slower rate relative to you. Since a faster spinning black hole has a smaller event horizon, in the first case, there would be a smaller event horizon.
Then how do scientists say that there are spinning and non-spinning black holes? Is that just in relation to Earth?
Ideas
First Idea
My first idea is also one that is more intuitive. When I move around the black hole, the black hole spins slower relative to me and consequently has a larger event horizon. In this idea, the black hole would just behave like a normal object. This would mean that if you went really fast around a black hole, you could get a lot closer to the black hole that if you were standing still.
This is kind of like a satellite that orbits Earth. The slower it moves, the easier it is to fall to the Earth. (I know this is a horrible analogy.)
Nothing special happens here.
Second Idea
My second idea is that when you move faster around the black hole, the relative rotational speed of the black hole doesn't change. Because of how fast it is/how dense it is and special relativity, moving around the black hole doesn't affect its speed.
This is like trying to accelerate past the speed of light.
No matter how much energy you spend, your speed barely changes.
I don't understand how this one would work. Why won't the rotational speed of the black hole stay the same?
Conclusion
What do black holes spin relative to? And what happens if you move around it? There are lots of questions that ask how black holes spin, or how fast they spin, but as far as I know, none of them address this question.
Best Answer
Actually, this is fundamentally incorrect. The spinning of the disk has nothing to do with the table in principle. Acceleration, including spinning, is not relative. It can be measured without reference to any external object. For example, using a ring interferometer, or a gyroscope.
It does not matter if the object is a disk or a black hole or anything else, spinning is not relative like inertial motion is.
The event horizon is a global and invariant feature of the spacetime. Your motion does not change it. Of course, you can use whatever coordinates you like and make the coordinate size change as you wish. However, which events are on the event horizon is unchanged by your motion.