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So-called 'hairless' black holes (no-hair theory, or theorem?) , which is what real black holes are, can be described by just three characteristics: Mass, spin, and charge.

It is easy enough to contemplate size and rotation, but what made astrophysicists or cosmologists believe a black hole might build up a charge?

I know that no black hole with a charge, or much if one, has been found, and the concept gets little mention in the news, but how did the idea first come up?

It is an electric charge we are talking about, right? Outside of the event horizon, correct?

I am confused....

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    $\begingroup$ Take a neutral black hole. Drop in a proton. Now what? $\endgroup$
    – J...
    Jul 12 at 19:10
  • $\begingroup$ As a side note, one of the reasons that this is of interest is that charging a black hole is potentially a way of violating the cosmic censorship conjecture. $\endgroup$
    – user15381
    Jul 13 at 0:41
  • $\begingroup$ Interesting... because for non-relativistic mind that I am, a black hole (an object without "hair", i.e. visible form) rotating is much harder concept than the electrically charged black hole (and yes, I know that the frame dragging is a thing and rotating black holes are conclusively observed) $\endgroup$
    – fraxinus
    Jul 13 at 7:49
  • $\begingroup$ @J...: It's gone? I know, we assume that the charge is conserved, but it's not like we have actually done the experiment with a real black hole. The argument why charge is conserved is ultimately theoretical. $\endgroup$
    – MSalters
    Jul 13 at 16:03
  • $\begingroup$ @MSalters Well, then the question is nothing about black holes and is entirely "Could the law of conservation of charge be wrong, and how?" A negative result here would imply crazy things, like photons having mass, etc. We could have a discussion about the possibility of extra dimensions "hiding" charge but I don't think that's where OP was going... $\endgroup$
    – J...
    Jul 13 at 16:43
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The answer is reasonably simple: (nearly) all matter consists of protons, neutrons and electrons, thus of either positively, or negatively charged particles or those with no charge.

The next step you need to make is to assume that for some reason whatsoever a black hole accretes more protons than electrons (or vice versa).

Such process might be envisionable, if you think of any process which produces a certain energy - which results in a much higher velocity for an electron than for a proton - so that effectively more protons might be captured. Any such process has an obvious end when the charge increased sufficiently much, such that the black hole starts to attract particles of the opposite charge in such numbers until both charges are again accreted equally. Should the charge separation and feeding process in its vicinity cease to function, it will slowly loose charge by attracting and thus accreting particles of the opposite charge until it again reaches zero charge.

So even if we haven't observed any, or even if we don't consider it likely to happen, it is a theoretical possibility which follows directly from the property of matter, given the elementary charge carried by some matter particles.

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    $\begingroup$ But note that this is expected to be a temporary phenomenon, since if the black hole builds up a electrical charge, it will preferentially attract oppositely charged particles, which will tend to reduce its net charge... $\endgroup$ Jul 12 at 11:58
  • $\begingroup$ Very true @PeterErwin. Any such process will level out at when the additional electrical attraction cancels the preference of whatever process to prefer one charge. $\endgroup$ Jul 12 at 12:08
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    $\begingroup$ I amended the middle paragraph by the gist of your comment $\endgroup$ Jul 12 at 15:28
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Formally, black holes are a prediction of Einstein's theory of gravity. They have been observationally confirmed.

Regarding theory: The field equations of Einsteinian gravity, the Einstein Field Equations, admit solutions. The first closed form solution of these equations was found in 1916 by Karl Schwarzschild which is the massive non-rotating, uncharged black hole with an event horizon. Then Reissner, Nordstrom, Weyl, and Jeffrey found the case of the non-rotating and charged black hole soon after. Compared to the Schwarszchild black hole which has its event horizon at the Schwarszchild radius, the Reissner-Nordstrom metric has two horizons (one event horizon and one Cauchy surface), the locations of which depend on the Schw radius and on the electric charge of the black hole. If the electric charge is equal or greater to the mass of the black hole (in units where G=c=1), then the black hole may form in nature but would be a naked singularity since the horizons no longer cover the physical singularity.

It is an electric charge we are talking about, right? Outside of the event horizon, correct?

Yes, electrostatic charge. The Reissner-Nordstrom metric assumes that all the mass and electric charge reside at the physical singularity of the black hole:

The assumption leads to the prediction that light from the outside universe concentrates infinitely at the inner horizon, which contradicts the assumption that the black hole is empty except at its singularity. In reality, if there were such a thing as a charged black hole, as you approached very close to its inner horizon, you would see a rapidly growing explosion of light from the outside universe. The light triggers the mass inflation instability. From the inner horizon on, the Reissner-Nordström geometry is not physically realistic, despite being an exact mathematical solution to Einstein's equations.

Several decades later, Roy Kerr discovered the solution for the general case of an uncharged, rotating black hole in the 1960s. Lastly, the solution for the charged, rotating black hole is called the Newman-Kerr black hole: so this one has mass, spin, and electric charge. See the table of types of black holes here.

It is not expected that black holes will form in nature with significant electric charge because electromagnetic repulsion in compressing an electrically charged mass is dramatically greater than the gravitational attraction (by about 40 orders of magnitude). Also, black holes can accrete material from their surroundings, and thus gain negative or positive charge, however the effect of accretion on the black hole's NET charge is negligible.

Regarding observation: Astrophysically, black holes are expected to have negligible charge, except in certain circumstances involving charged particle phenomena near black holes, e.g. cosmic rays, but they are expected to have spin! And we've observed lots of black holes now, stellar mass black holes in X-ray binaries and in binary merger events, and supermassive black holes in galactic nuclei.

It is possible that all of the black holes that we've discovered thus far DO have electric charge, but that it is so small that its very difficult for us to measure currently, so we don't know if they have charge or not. Future observations are being explored for trying to measure the electric charge of a black hole, for example this framework uses retro-lensing.

Concerning observations of the astrophysical formation of black holes, all observations to date indicate that the Kerr metric is the correct description of black holes that form in nature. This is why we currently consider the no-hair theorem to be valid, along with the astrophysical expectation of negligible electric charge, although it is still unproven in full generality. Future observations of black hole electric charge could force us to update this picture, however! IF that happens, then the Kerr-Newman metric would replace the Kerr metric as the best description we have for black holes in nature.

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  • $\begingroup$ All the metrics above are static. Doesn't that mean that none of them deal (accurately) with the accretion of mass or charge. $\endgroup$
    – ProfRob
    Jul 12 at 15:14
  • $\begingroup$ Hmmm... I'm not sure. As far as I understand, once you add fluid dynamics for the accretion disk, the( disk+Kerr background) spacetime is no longer static, and as far as I understand, fully general relativistic numerical simulations can handle this (nowadays), of course not perfectly. Perhaps I'm not understanding your point? $\endgroup$ Jul 12 at 16:46
  • $\begingroup$ Just that you simultaneously talk about the Kerr-Newman metric and black holes accreting from their surroundings to become charged. There's something missing in the explanation. To an external observer, and in a static metric, nothing can be accreted through the event horizon, so the BH couldn't become charged. Is there some equivalent to Birkhoff's theorem that can be appealed to? $\endgroup$
    – ProfRob
    Jul 12 at 18:08
  • $\begingroup$ In my answer, I really just meant that a black hole will accrete positive and negative charges in principle, and this works to keep the net charge of the black hole very small. The effect you're referring to with the external observer is an example of a loss of simultaneity, and we can't see exactly at the event horizon of an accreting black hole anyway in principle. However, measurements by the event horizon telescope of the shadow of a supermassive black hole agrees well with the predictions of the Kerr spacetime geometry, though future measurements might shed more light! ;) $\endgroup$ Jul 12 at 18:39
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    $\begingroup$ Can the electric field lines starting within the event horizon of a charged black hole reach space outside the event horizon? The way I understand black holes (badly, I presume) they shouldn’t, and so there should be no measurable charge outside of the black hole. What am I missing? $\endgroup$
    – Seb
    Jul 12 at 23:37
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As matter is neutral in general black holes will be neutral in general too. Bodies that are prone to becoming a black hole are neutral too. A neutron star is neutral wrt electric charge. For a charged black hole to develop charge would very much act against this forming. Matter would be repulsed before gravitational collapse.

Charged BH's are a mere hypothetical curiosity (that is, charged BH's with a considerable thick hair). They exist in theory only. With one hair extra. Real BH's have only a mass and a rotational hair. Though there are theories giving them soft hair. In order to solve the information paradox. Some even propose a firewall.

A maximally charged black hole is a naked one. Its event horizon lies at infinity due to the energy contained in the electric field outside the charge. Well, even if maximally charged the hole has a horizon. But if the elementary charge were bigger the horizon goes to infinity.

Black holes with charge have not been observed but with magnetic fields are almost certainly common. The super massive one in M87 is seen as one with massive magnetic fields. As can be expected of these gargantuans. Plasma whirls around in these fields.

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    $\begingroup$ Where did you get this information from? Please edit your post to include your references. $\endgroup$ Jul 15 at 1:58

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