I Measuring Charge & Angular Momentum in Black Holes

[CalcNerd]

It is stated that a Black hole has only mass, angular momentum and charge for properties, but since it is black ie no light escapes its event horizon and charge E/M is related (same speed) as light (photons), how can unbalanced charge be detected?

And since many Black holes have electron clouds ejected out from the poles, one could speculate that these black holes would be positively charged. Can this actually be measured, since light cannot escape the horizon, how can we really observe a charge?

Since I'm asking, let's also talk about angular momentum. Since all the mass is mathematically located at a singularity, how can a black hole have angular momentum? Or is this an argument to state that the mass of the black hole cannot be located at a single point, due to the BH having angular momentum?

Thank you in advance for your input.

 

[Drakkith]

It is stated that a Black hole has only mass, angular momentum and charge for properties, but since it is black ie no light escapes its event horizon and charge E/M is related (same speed) as light (photons), how can unbalanced charge be detected?

Imagine a charged particle falling into a black hole. As it approaches the event horizon time dilation gradually increases. To a far away observer the charge never passes the event horizon and so its effect on the EM field never disappears. That's one way to look at it.

And since many Black holes have electron clouds ejected out from the poles, one could speculate that these black holes would be positively charged.

I expect that this is from the accretion disk, not from anything having to do with charges passing the event horizon.

Since I'm asking, let's also talk about angular momentum. Since all the mass is mathematically located at a singularity, how can a black hole have angular momentum? Or is this an argument to state that the mass of the black hole cannot be located at a single point, due to the BH having angular momentum?

That one I can't answer.

 

[Vanadium 50]

A BH with charge and angular momentum will have a magnetic field. You could also tell via frame-dragging.

 

[kimbyd]

It is stated that a Black hole has only mass, angular momentum and charge for properties, but since it is black ie no light escapes its event horizon and charge E/M is related (same speed) as light (photons), how can unbalanced charge be detected?

No gravitons can escape either, but it still has a gravitational field. Drakkith's answer is one way to understand how this can possibly work.

And since many Black holes have electron clouds ejected out from the poles, one could speculate that these black holes would be positively charged. Can this actually be measured, since light cannot escape the horizon, how can we really observe a charge?

These particle streams are particles which never entered the event horizon of the black hole. A spinning black hole has an "ergosphere" which is a bulge just outside the event horizon. The gravitational and magnetic properties inside this bulge direct a good amount of matter which falls into that region out the poles at extreme velocity. I don't think there's much of any change in net charge of the black holes due to this process. Even if they did, it's expected that under realistic conditions they'll discharge rapidly.

Since I'm asking, let's also talk about angular momentum. Since all the mass is mathematically located at a singularity, how can a black hole have angular momentum? Or is this an argument to state that the mass of the black hole cannot be located at a single point, due to the BH having angular momentum?

The singularity isn't a real thing. Think of the interior of a black hole as a system where there's a sphere somewhere inside that is the end of the accuracy of General Relativity's correctness. We don't know exactly where that sphere is. It's probably within the black hole (since black holes seem to have properties which make sense from General Relativity so far). But we don't know where within the black hole. Anything that's going on inside that sphere is described by some other theory. We don't yet know which one.

That said, the angular momentum of the black hole depends upon all of the matter which has fallen into it. The data about that matter is imprinted on the horizon, including its angular momentum. So the horizon alone provides sufficient information about its angular momentum, regardless of the internal configuration.

 

[CalcNerd]

Thanks for the responses. I do grasp the concept of a BH having angular momentum with the argument that the interior of a BH is not a true singularity, but that we don't have the current theory to actually describe its interior yet.

However, I am still having difficultly with the idea of charge (and gravitons too) being able to escape the BH. Actually, observation seems to show that electrons are ejected from the incoming matter along the poles of BH. Wouldn't that imply the BH is accumulating a positive charge. And the positive charge would quickly result in the shutdown of further electrons being ejected from the poles of the BH? However if the BH is neutral charge, electrons can continue to be ejected from the BH without shutting down.

As matter is accelerated around the BH, the matter surely breaks down into a plasma with the escape velocity of the electrons being much easier as it is 1/1800th the mass of protons or neutrons. If the BH had charge, wouldn't it simply grab all of the plasma and not selectively eject the electrons?

 

[PeterDonis]

I am still having difficultly with the idea of charge (and gravitons too) being able to escape the BH.

They don't. Charge and mass are not properties of anything inside the hole; they are properties of the spacetime around the hole. One way of seeing how that works is to note that, according to GR, all of the properties of spacetime at any given event can only depend on things in the past light cone of that event. Nothing inside the black hole is inside the past light cone of any event outside the hole. But the original matter that collapsed to form the hole (as well as any electric charge it carried) is in the past light cone of events outside the hole. So is any matter and charge that falls into the hole after it forms. It is the mass (more precisely stress-energy) and charge contained in those regions of spacetime--the region containing the matter and charge that originally collapsed to form the hole, and containing any objects that fall into the hole later, before any of those things cross the hole's horizon--that is the actual source of the gravity and charge that you, at some event outside the hole, feel.

Note that the above analysis is entirely classical. Your use of the term "graviton" indicates that you are thinking of this at least partially in quantum terms; but any quantum aspects of this should really be discussed in a separate thread in the Quantum Physics forum (and discussion will be limited since we don't have a good theory of quantum gravity so there's not a lot we can say about the topic). Before starting any such thread, though, you might want to read this article by John Baez, which, while very brief, gives a good overview of the topic:

http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/black_gravity.html

I think there are also previous threads discussing this topic (both classical and quantum) here on PF, but I can't find them right now.

 

[PeterDonis]

let's also talk about angular momentum. Since all the mass is mathematically located at a singularity, how can a black hole have angular momentum? Or is this an argument to state that the mass of the black hole cannot be located at a single point, due to the BH having angular momentum?

Your last sentence here is correct. Angular momentum is in fact also a property of the spacetime around the hole, not a property of anything inside the hole. (Also note that it is not the case that all of the mass is at the singularity; it isn't, as my previous post should make clear. It's not even the case that all of the matter that collapsed to form the hole is located at the singularity. The singularity is a future endpoint to spacetime inside the hole; classically speaking, anything that hits it gets destroyed and stops existing. One of the key issues in developing a theory of quantum gravity is how quantum effects change that classical prediction.)

 

[kimbyd]

However, I am still having difficultly with the idea of charge (and gravitons too) being able to escape the BH. Actually, observation seems to show that electrons are ejected from the incoming matter along the poles of BH.

Why do you think it's just electrons?