[zaarn]

The spin axis isn't a valuable reference since it depends on your frame of reference, which is a concept that gets rather ambiguous as you get close to a black hole anyway.

Plus you can just "rotate" a black hole to get it to have the same spin axis as another black hole. You can't "rotate" or "translate" a black hole in space to make the other three numbers change. Those require ingesting matter or emitting hawking radiation and that is the only thing that changes those properties.

[bell-cot]

I'm figuring that the low-rent planets, stars, etc. in the vague vicinity of an actual black hole would provide a fine frame of reference.

> Plus you can just "rotate" a black hole to get it to have the same spin axis as...

Quip: If you have the tech & budget to meaningfully rotate a spinning black hole, then you've got the tech & budget to change the other parameters, too.

FWIW - Wikipedia's answer is that 11 numbers (or 2 scalars and 3 vectors) are needed to fully spec. a stable black hole - https://en.wikipedia.org/wiki/Rotating_black_hole#Types_of_b...

[zaarn]

There is a cheap and even for current humanity achievable way to rotate a black hole; change your frame of reference. That is not only true for angular momentum but linear momentum and position. Those are entirely dependent on the observer and their frame of reference. Spin, magnetic charge and mass are not.

Two black holes who differ only by their position, linear and/or angular momentum but are equal in all other parameters are not distinguishable from simply seeing the same black hole twice from a different perspective.

Two black holes who differ in any of the three properties of mass, spin or magnetic charge are distinguishable by those properties (but even that is arguable to some extend).

edit: The rent prices of a planet don't matter since frame of reference is an actual term here, there is no frame of reference more valid than any other for determining the linear or angular velocity or the position of a black hole.