| > A black hole only has three properties, in our current understanding of general relativity - but "electrical charge" is one of those properties An isolated black hole, at a suitable coordinate time, has mass, electric charge, angular momentum (three components), linear momentum (three components) and spatial position (three components). Holding the BH at the spatial origin drops the last six. Also, a slight wrinkle: this state is asymptotic -- at timescales less than light-crossing there can be substantial additional hair. At longer timescales, some configurations can persist on much longer than light-crossing scales -- one example is the magnetic field at the newly formed horizon of a isolated collapsed rotating magnetar. "isolated" here can get tricky in practice as well. But in the usual case, no, you can't look at a black hole and tell whether someone much earlier threw (classical picture) in one shell of matter of mass M vs two concentric shells of matter at 1/2 M each or three concentric shells of matter of 1/4 M, 1/2 M and 1/4 M (or 1/2 M, 1/4 M and 1/4 M, etc.). But what's this shells picture for non-negligible charge? (Switching to a dust doesn't help, fwiw). More formally, the no-hair theorem says that in a stationary electrovacuum, a black hole solution takes on a specific form. That mostly means that we should be able to perturb a Kerr-Newman BH solution and get the right results for an astrophysical BH. |
>at timescales less than light-crossing there can be substantial additional hair.
Ahh, thank you - that clears up some misconceptions of mine that have always confused me, like "Wait, so if black holes have no hair, how can they wobble and ring-down and produce gravitational waves after a black hole merger?"