Charged Black Hole

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alexh123456789
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Charged Black Hole

Postby alexh123456789 » Sun Feb 08, 2009 5:08 pm UTC

How is it possible for black holes to have an electric charge if nothing can escape them? I've read that electromagnetism is caused by the exchange of virtual photons but how can these escape the black hole?

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Re: Charged Black Hole

Postby theoreticallyKat » Sun Feb 08, 2009 5:21 pm UTC

I'm no expert, and I don't know about EM charge of a black hole. But I heard a theory that If a virtual pair of particles is created next to a black hole one may "fall in" and the other may escape, becoming a real particle. i.e. the event horizon is between the two.Image
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Re: Charged Black Hole

Postby parallax » Sun Feb 08, 2009 6:51 pm UTC

There would be an electromagnetic field around the black hole, outside the event horizon.
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Re: Charged Black Hole

Postby alexh123456789 » Sun Feb 08, 2009 9:01 pm UTC

My question came from this. I know about hawking radiation but I'm asking how the black hole's electromagnetic field escapes its gravity and is detected. I might just be misinterpreting it though or have some misconception about EMF's

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Re: Charged Black Hole

Postby doogly » Sun Feb 08, 2009 9:12 pm UTC

The electric field still exists outside because in all your favorite black hole metrics (like RN) the black holes are eternal in the past. You don't take into account information traveling from the interior to the exterior because the field always existed.

For a realistic black hole, it wasn't always a black hole. It was probably a star (or whatever those supermassive guys came from) that had some net charge. It collapses, and gets a net charge in the inside, and the field outside remembers what this net charge was. Now if some new charge comes along anybody outside will not see that charge as coming from the center, but rather still caught somewhere in the accretion disc. If you find yourself caught inside a black hole, only realizing your fate after you have crossed the horizon, and want communicate a last message to your loved ones and try to do it by radiating a pattern in the electromagnetic field, rest assured that it will not reach them.
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Re: Charged Black Hole

Postby alexh123456789 » Sun Feb 08, 2009 9:20 pm UTC

Ok, that kind of makes sense but I didn't know that electric fields could remember after the charge was separated. Would you explain what an electric field actually is, because I don't see how it's possible for the field to remain after the charged particles were separated (put into the black hole).

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Re: Charged Black Hole

Postby doogly » Sun Feb 08, 2009 9:40 pm UTC

Aaaaaah, it's a field. Fields are there own kind of thing and I'm not sure what more this to explaining what one "is." It flows more logically the other way, that particles are quantised bits of a field. The field concept is more fundamental than the particle one. This probably isn't helpful, maybe someone else can do better.

Static fields like the ones in RN don't radiate away. They just hang around and don't go anywhere. You can get ones that do radiate in other situations, like an accelerating charge.
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Re: Charged Black Hole

Postby wisnij » Sun Feb 08, 2009 9:41 pm UTC

alexh123456789 wrote:Ok, that kind of makes sense but I didn't know that electric fields could remember after the charge was separated. Would you explain what an electric field actually is, because I don't see how it's possible for the field to remain after the charged particles were separated (put into the black hole).

Picture a distant observer watching an object fall into a black hole. As it gets closer and closer to the event horizon, the time dilation gets more and more extreme until time nearly appears to stop for that object (as measured by our hypothetical observer far away). It would seem to hover there, just over the event horizon, frozen in place forever. In other words, as far as the rest of the universe is concerned, that object never actually crosses the event horizon.

Now, what if that object is electrically charged? Well, as for gravity, changes in the electromagnetic field propagate at lightspeed. (Hardly surprising, as light itself is such a change. ;)) So as long as the object remains "visible" to the rest of the universe, its charge will still contribute to the electrical field. If it helps, you can picture electric field lines coming off the particle like strings or wires; even as it falls towards the hole, those lines still extend outwards towards infinity.

To clarify further: a field is just some quantity that has a value at every point in space. Fields fill all space by definition. A charged particle doesn't "have a field"; rather, it affects the value of the electric field, with the magnitude of that effect depending on how far from the particle you measure it.

theoreticallyKat wrote:I'm no expert, and I don't know about EM charge of a black hole. But I heard a theory that If a virtual pair of particles is created next to a black hole one may "fall in" and the other may escape, becoming a real particle. i.e. the event horizon is between the two.

This is kind of a separate issue; that's usually given as an explanation of Hawking radiation. But it's worthwhile to note that the underlying physics is even more fascinating.
Last edited by wisnij on Mon Feb 09, 2009 3:28 am UTC, edited 4 times in total.
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Re: Charged Black Hole

Postby theoreticallyKat » Sun Feb 08, 2009 10:02 pm UTC

OK lesson learnt, don't post crap about stuff I haven't learnt yet...there will be someone on here that knows ALOT more. :D
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Re: Charged Black Hole

Postby doogly » Sun Feb 08, 2009 10:11 pm UTC

theoreticallyKat wrote:OK lesson learnt, don't post crap about stuff I haven't learnt yet...there will be someone on here that knows ALOT more. :D


Oh, you don't have to stop, there's always the chance you can explain the stuff you do know better! There might even be a rather good chance of this, especially if people keep asking about fields and I start talking about C* algebras. Nobody wants that.
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Re: Charged Black Hole

Postby gmalivuk » Mon Feb 09, 2009 1:41 am UTC

These forums are typically pretty easy on people who, with good intentions, post about something that isn't actually helpful to whoever was asking the original question. So yeah, don't worry about it. No one will rip you a new one for posts like the earlier one you made.

(What *does* tend to more frequently piss other people off is when someone comes into the middle of an ongoing discussion with an attitude like they already know more than anyone else there could possibly imagine...)
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Re: Charged Black Hole

Postby PM 2Ring » Mon Feb 09, 2009 9:52 am UTC

What wisnij said also applies to how the black hole's gravity "gets out".

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

How does the gravity get out of the black hole?

Purely in terms of general relativity, there is no problem here. The gravity doesn't have to get out of the black hole. General relativity is a local theory, which means that the field at a certain point in spacetime is determined entirely by things going on at places that can communicate with it at speeds less than or equal to c.

If a star collapses into a black hole, the gravitational field outside the black hole may be calculated entirely from the properties of the star and its external gravitational field before it becomes a black hole. Just as the light registering late stages in my fall takes longer and longer to get out to you at a large distance, the gravitational consequences of events late in the star's collapse take longer and longer to ripple out to the world at large. In this sense the black hole is a kind of "frozen star": the gravitational field is a fossil field. The same is true of the electromagnetic field that a black hole may possess.

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Re: Charged Black Hole

Postby Matterwave1 » Mon Feb 09, 2009 10:13 pm UTC

Doesn't time dilation only tend towards infinity as you get to the singularity?

The time dilation at the event horizon should be significant, but not infinite...right? What about super-massive black holes with Event Horizons which are very far from the singularity?

I'm not sure how gravitational time dilation works, so I could be very, very wrong :P

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Re: Charged Black Hole

Postby wisnij » Tue Feb 10, 2009 12:01 am UTC

Matterwave1 wrote:Doesn't time dilation only tend towards infinity as you get to the singularity?

To an outside observer, coordinate time goes to infinity as you approach the event horizon. Everything within the event horizon is cut off from the rest of the universe; our hypothetical observer can't measure anything in there.
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Re: Charged Black Hole

Postby parallax » Tue Feb 10, 2009 1:05 pm UTC

Remember that in relativity, different observers can have different notions of time. Part of the reason that black holes are confusing is that different observers have very different notions of time. If a particle falls into a black hole, an observer far away from the black hole would calculate it as getting closer and closer to the event horizon but never crossing it. An observer falling into the black hole with the particle would see it cross the horizon in a finite time and then hit the singularity, also in finite time.
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Re: Charged Black Hole

Postby wisnij » Tue Feb 10, 2009 3:28 pm UTC

^ What he said. ;)
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Re: Charged Black Hole

Postby Iv » Wed Feb 11, 2009 4:36 pm UTC

wisnij wrote:Picture a distant observer watching an object fall into a black hole. As it gets closer and closer to the event horizon, the time dilation gets more and more extreme until time nearly appears to stop for that object (as measured by our hypothetical observer far away). It would seem to hover there, just over the event horizon, frozen in place forever. In other words, as far as the rest of the universe is concerned, that object never actually crosses the event horizon.

Well, as it seems to "freeze", shouldn't it stop emitting light, too ? I am not knowledgeable to transpose this reasoning in "emission" of "quantum of electrical interactions" or "quantum of gravitational interactions" but I never looked at it this way. "fossil fields"... wow... :shock:

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Re: Charged Black Hole

Postby gmalivuk » Fri Feb 13, 2009 2:56 pm UTC

Iv wrote:Well, as it seems to "freeze", shouldn't it stop emitting light, too ?

And it does, asymptotically. The light being emitted or reflected from an infalling object gets more and more redshifted as time goes on.
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Re: Charged Black Hole

Postby Iv » Fri Feb 13, 2009 3:42 pm UTC

I always thought that fields were an abstraction for particle exchanges. Apparently something is wrong in this view, as gravity exists outside a black hole without particles coming out from them.

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Re: Charged Black Hole

Postby doogly » Fri Feb 13, 2009 3:51 pm UTC

Yeah, it's more the other way around. Particle interactions are a way to get a good handle on field interactions, but the particle concept is less fundamental. In curved space the particle content is not really well defined, you get inequivalent vacua, Unruh effect, all kinds of good stuff. If your space is asymptotically flat (like for black hole metrics) you can still define a lot of your particle concepts, like an S matrix and such, but not in general.

But also, these particle exchanges aren't needed for communication of a static field. If you enter a black hole and then shoot off some gravity waves, they won't reach anyone outside the black hole. People outside will only see
- you from before you fell in
- the black hole's initial state, which was defined when it collapsed
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Re: Charged Black Hole

Postby Iv » Fri Feb 13, 2009 4:17 pm UTC

doogly wrote:But also, these particle exchanges aren't needed for communication of a static field. If you enter a black hole and then shoot off some gravity waves, they won't reach anyone outside the black hole. People outside will only see
- you from before you fell in
- the black hole's initial state, which was defined when it collapsed

Except they won't "see" me as in "receive photons emitted/reflected by my spaceship" as light will eventually cease to reach them (its intensity will asymptotically decrease but still). But they still will be able to sense my gravitational and electrical fields which will stay constant in time ?

Also a funky and somehow unrelated question : are circular linear singularities possible ? Could they form toroidal event horizons ?

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Re: Charged Black Hole

Postby doogly » Fri Feb 13, 2009 4:30 pm UTC

They'll keep seeing you, they just won't see you 'update.' You'll never disappear from their vision though.

You get rings of singularity in spinning black holes. This is the Kerr metric. The event horizon isn't a torus though, it's just an ellipse. In five dimensions though, you can get a black ring, maybe you've seen discussion of one of these looking for toroidal black holes before?
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Re: Charged Black Hole

Postby wisnij » Fri Feb 13, 2009 8:30 pm UTC

Iv wrote:
wisnij wrote:Picture a distant observer watching an object fall into a black hole. As it gets closer and closer to the event horizon, the time dilation gets more and more extreme until time nearly appears to stop for that object (as measured by our hypothetical observer far away). It would seem to hover there, just over the event horizon, frozen in place forever. In other words, as far as the rest of the universe is concerned, that object never actually crosses the event horizon.

Well, as it seems to "freeze", shouldn't it stop emitting light, too ? I am not knowledgeable to transpose this reasoning in "emission" of "quantum of electrical interactions" or "quantum of gravitational interactions" but I never looked at it this way. "fossil fields"... wow... :shock:

When I say the observer "sees" something in this context, I don't mean that literally -- light is quantized, so the time until the outside observer measures the last actual photon coming off of the infalling object is finite. To quote the FAQ again:

Matt McIrvin wrote:Now, this led early on to an image of a black hole as a strange sort of suspended-animation object, a "frozen star" with immobilized falling debris and gedankenexperiment astronauts hanging above it in eternally slowing precipitation. This is, however, not what you'd see. The reason is that as things get closer to the event horizon, they also get dimmer. Light from them is redshifted and dimmed, and if one considers that light is actually made up of discrete photons, the time of escape of the last photon is actually finite, and not very large. So things would wink out as they got close, including the dying star, and the name "black hole" is justified.

As an example, take the eight-solar-mass black hole I mentioned before. If you start timing from the moment the you see the object half a Schwarzschild radius away from the event horizon, the light will dim exponentially from that point on with a characteristic time of about 0.2 milliseconds, and the time of the last photon is about a hundredth of a second later. The times scale proportionally to the mass of the black hole. If I jump into a black hole, I don't remain visible for long.


That said, the object can still have a measurable effect on the outside universe through other means, such as the electric or gravitational field. I generally try to say "observe" or "measure" instead of "see" to avoid this ambiguity, but sometimes I slip up. :|
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Re: Charged Black Hole

Postby hitokiriilh » Wed Feb 18, 2009 4:15 pm UTC

Meh. I don't like some of these explanations. For instance, saying that black holes can have a field only because they were charged before collapse isn't right. This would imply black holes can't neutralize by absorbing particles of the opposite charge...but models show black holes can neutralize. Here's a better explanation:

From a field theoretic perspective, the Coulomb field is comprised of virtual photons - i.e. photons that are not 'on (mass) shell' in momentum space. This means the virtual particles can move slower or faster than the speed of light (Coulomb scattering in field theory involves an integral over all mometum space of something called the 'photon propagator' so all of the faster and slower than light virtual photons are accounted for.). Things can't escape from a black hole because the light cone 'tips' towards the center of the black hole as you traverse the event horizon. If things move more slowly than the speed of light, you can't escape...period. But if you have something off-shell it can propagate otuside the lightcone. So LIGHT (E&M waves that are ON shell) can't escape, but Coulomb fields and such can.

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Re: Charged Black Hole

Postby hitokiriilh » Wed Feb 18, 2009 4:22 pm UTC

alexh123456789 wrote:Ok, that kind of makes sense but I didn't know that electric fields could remember after the charge was separated. Would you explain what an electric field actually is, because I don't see how it's possible for the field to remain after the charged particles were separated (put into the black hole).


They can't. The Coulomb fields still extract information about the black hole's charge. See above.

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Re: Charged Black Hole

Postby doogly » Wed Feb 18, 2009 4:32 pm UTC

Which models are these? Do they neutralize completely? I would have suspected you get something like a multipole, with some charge inside and the neutralizing parts making their way in, but still always appearing to be outside.
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Re: Charged Black Hole

Postby hitokiriilh » Wed Feb 18, 2009 4:37 pm UTC

doogly wrote:Which models are these? Do they neutralize completely? I would have suspected you get something like a multipole, with some charge inside and the neutralizing parts making their way in, but still always appearing to be outside.


Truth be told I just parroted a lecturer at SPS last week. In retrospect I wish I had asked about the model. It makes sense if we talk about local fields and such and follow a particle falling into a black hole using proper time and ask "in the singularity's reference frame, what's its charge?" it would depend on the stuff that fell in...but what an external observer sees is indeed another matter.

Nonetheless, the fields 'escape' because of the whole off-mass-shell thing.

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Re: Charged Black Hole

Postby wisnij » Wed Feb 18, 2009 7:21 pm UTC

hitokiriilh wrote:Meh. I don't like some of these explanations. For instance, saying that black holes can have a field only because they were charged before collapse isn't right. This would imply black holes can't neutralize by absorbing particles of the opposite charge...but models show black holes can neutralize.

I don't think anyone's saying that, though. Black holes would start off charged if they collapsed from a body with net charge, sure. But if any new charge falls in, its field gets added to the pre-existing one as it asymptotically approaches the event horizon (as measured by a distant observer). If that happens enough the hole will still neutralize.
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