Charge of Black Holes: Measurability & Effects

[ehj]

I was wondering about something.
If a black hole has charge, would it be measureable? Does the electric field escape the black hole even when light cannot?
Or if the field does not escape the black hole, how do we know that it's a charged black hole?

 

[lzkelley]

Thats a really interesting question. We can definitely predict that black-holes have charge, based on conservation of charge - i.e. for that conservation to hold, BH's would have to have some net charge.
I really don't think that electric fields can emanate from the interior of a black-hole (not only because E&M forces are conveyed by photons which can't escape; but also because those fields have mass - and would be pulled back in). But I'm curious to hear from others. Could/would E&M fields exist from the event horizon? - i.e. before particles pass the event horizon?

 

[pmb_phy]

I was wondering about something.
If a black hole has charge, would it be measureable? Does the electric field escape the black hole even when light cannot?
Or if the field does not escape the black hole, how do we know that it's a charged black hole?

Just because a black hole is charged doesn't mean that the charge resides within the event horizon. If it does then I don't see a problem with the electric field since the field is not moving and thinking of it as "escaping" seems erroneous to me.

Pete

 

[ehj]

Just because a black hole is charged doesn't mean that the charge resides within the event horizon.

Well if the charge isn't within the event horizon that would imply that the charge has been separated from the matter from which it originates? That sound's odd.

If it does then I don't see a problem with the electric field since the field is not moving and thinking of it as "escaping" seems erroneous to me.

Well I just wan't to know if there's any way that an observer would know if the black hole is charged or not, without knowing what went into it in the past.

 

[JesseM]

Apparently in quantum field theory virtual photons (associated with electromagnetic forces) can escape the black hole even if measurable non-virtual photons (associated exclusively with electromagnetic waves) cannot--see the discussion from How does the gravity get out of the black hole?:

Gravitons don't exist in general relativity, because GR is not a quantum theory. They might be part of a theory of quantum gravity when it is completely developed, but even then it might not be best to describe gravitational attraction as produced by virtual gravitons. See the physics FAQ on virtual particles for a discussion of this.

Nevertheless, the question in this form is still worth asking, because black holes can have static electric fields, and we know that these may be described in terms of virtual photons. So how do the virtual photons get out of the event horizon? Well, for one thing, they can come from the charged matter prior to collapse, just like classical effects. In addition, however, virtual particles aren't confined to the interiors of light cones: they can go faster than light! Consequently the event horizon, which is really just a surface that moves at the speed of light, presents no barrier.

I couldn't use these virtual photons after falling into the hole to communicate with you outside the hole; nor could I escape from the hole by somehow turning myself into virtual particles. The reason is that virtual particles don't carry any information outside the light cone. See the physics FAQ on virtual particles for details.

 

[ehj]

... but also because those fields have mass

So the EM field has mass, but is according to JesseM unaffected by gravity? Isn't that a contradiction? Do these two statements come from different theories, or maybe one of the statements doesn't come from any theory ;P?

 

[pmb_phy]

Well if the charge isn't within the event horizon that would imply that the charge has been separated from the matter from which it originates? That sound's odd.

That wasn't what I meant. I said that a black hole can be charged but have the charges piled up just outside its event horizin. The matter is not separated from the charge. The charged matter is located where the charge is. Think of a uniform charge density sitting just outside the event horizon like a bunch of electrons spread out just outside of the event horizon.

Well I just wan't to know if there's any way that an observer would know if the black hole is charged or not, without knowing what went into it in the past.

Yes. Measure the electric field around the black hole and that will tell you whether the black hole is charged or not.

Pete

 

[pmb_phy]

So the EM field has mass, but is according to JesseM unaffected by gravity?

Since when? An EM field is both affected by gravity and can generate a gravitational field.

Pete

 

[JesseM]

So the EM field has mass, but is according to JesseM unaffected by gravity?

The article I quoted didn't say virtual photons were "unaffected by gravity", just that they can escape the event horizon (the virtual particle FAQ mentions that when summing over all possible virtual particle paths, one includes FTL paths). Quantum field theory on a curved spacetime background does give different results than in flat spacetime, I believe.

 

[gendou2]

I imagine that any E-field or B-field lines originating inside the event horizon do not cross it, because they are drawn in space which is curved to infinity in that region.

 

[pmb_phy]

I imagine that any E-field or B-field lines originating inside the event horizon do not cross it, because they are drawn in space which is curved to infinity in that region.

The spacetime curvature inside the event horizon is finite everywhere except the origin. Other infinities are coordinate infinities and do not represent a physical infinity.

Pete

 

[ehj]

I said that a black hole can be charged but have the charges piled up just outside its event horizin. The matter is not separated from the charge. The charged matter is located where the charge is. Think of a uniform charge density sitting just outside the event horizon like a bunch of electrons spread out just outside of the event horizon.

Pete

I might not have been clear on this, but what I was interested in knowing was what would happen to the field if the matter the black hole is made of, the core of the black hole, is made up of charged matter (not purely). It is obvious that charge outside the event horizon would generate a measureable electric field, so I didn't think this was what you meant.

 

[pmb_phy]

I might not have been clear on this, but what I was interested in knowing was what would happen to the field if the matter the black hole is made of, the core of the black hole, is made up of charged matter (not purely). It is obvious that charge outside the event horizon would generate a measureable electric field, so I didn't think this was what you meant.

It is my understanding that it is impossible for an outside observer to tell the difference. It was for that reason that I used that as an example.

Pete

 

[ehj]

ah :)

 

[gendou2]

The spacetime curvature inside the event horizon is finite everywhere except the origin. Other infinities are coordinate infinities and do not represent a physical infinity.

Pete

Oh, you're right! Thanks for catching my mistake.
In that case, how might the E-field lines best be drawn?

 

[captain]

So the EM field has mass, but is according to JesseM unaffected by gravity? Isn't that a contradiction? Do these two statements come from different theories, or maybe one of the statements doesn't come from any theory ;P?

i have a somewhat stupid question but how do E&M fields have mass if they are made up of photons and photons are considered to be massless or is it that photons have an indeterminant relativistic mass that is non zero. Can someone elaborate for me?

 

[schieghoven]

The Kerr-Newman metric describes a charged black hole, in the sense that the electric flux through a surface surrounding the black hole is nonzero (i.e at large distances the electric field lines point radially away from the black hole). I'm not sure what the electric field looks like near the horizon.

http://en.wikipedia.org/wiki/Kerr_metric

Dave

 

[gendou2]

i have a somewhat stupid question but how do E&M fields have mass if they are made up of photons and photons are considered to be massless or is it that photons have an indeterminant relativistic mass that is non zero. Can someone elaborate for me?

Photons have zero rest mass, and zero gravitational field.
From E=mc² we can find a equivalent mass of any photon.
Since photons have energy, they have an equivalent mass.
This equivalent mass is responsible for their momentum.

Further reading:
http://www.Newton.dep.anl.gov/askasci/phy00/phy00332.htm
http://en.wikipedia.org/wiki/Mass-energy_equivalence

 

[lzkelley]

Photons do have mass, just not rest mass (and the mass is easily determinable depending on the frequency - as i recall).

The concepts of fields and of the gauge bosons that convey the forces are 2 somewhat different things; its my understanding that they don't coexist in a single interpretation of what used to be "action-at-a-distance"... what i mean is, either you can look at it as fields, or you can look at it as photons - not positive about that - but I'm sure any observable (like mass) could be consolidated between the two.

Fields have mass because they have to have momentum - i can't remember why/how to prove that (sorry). And this is consolidated with gauge because the photons conveying the forces also have mass.

 

[blackwing1]

Black holes do have charge because the angular momentum, mass, and charge of any particles that are sucked in are retained by the black hole itself.

 

[pmb_phy]

Photons have zero rest mass, and zero gravitational field.

That is incorrect. Light most certainly does generate a gravitational field. Take a look at the second link that you posted because it says

Note further that in accordance with Einstein’s Strong Equivalence Principle (SEP), all forms of mass and energy produce a gravitational field in the same way.[7] So all radiated and transmitted energy retains its mass.
...
Wien went on by stating, that if it is assumed that gravitation is an electromagnetic effect too, than there has to be a strict proportionality between (electromagnetic) inertial mass and (electromagnetic) gravitational mass.

Why would you believe otherwise??

From E=mc² we can find a equivalent mass of any photon.

What you call an equivalent mass is what is known as inertial mass aka relativistic mass.

Since photons have energy, they have an equivalent mass.

When you state it that way it gives the impression that "equivalenc" mass is somehow different that the "real" mass (whatever "real" means)

Notice that your second link contains the following comment.

Even a single photon traveling in empty space has a relativistic mass, which is its energy divided by c².

Before one addresses the question regarding whether a photon/light has mass or not you really must state what definition you are using. A photon has an inertial mass (since it has momentum) a passive gravitational mass (since it is affected by gravity) and an active gravitational mass (since it can generate a gravtiational field).

Pete

 

[ehj]

It is my understanding that it is impossible for an outside observer to tell the difference.
Pete

I still don't think I've found a satisfying answer as to why the EM field can escape from the interior of a black hole, passing the event horizon. Why is it your understanding that it is impossible for an outside observer to tell the difference whether the charge is located in the core of the black hole, or on the event horizon? The quantum explanation (what you linked) seems to be saying, in short, that "the EM field can pass the event horizon because the virtual particles conveying the force, can pass the event horizon" which doesn't really solve the problem, just introduces some new particles with peculiar properties.

 

[pmb_phy]

I still don't think I've found a satisfying answer as to why the EM field can escape from the interior of a black hole, passing the event horizon. Why is it your understanding that it is impossible for an outside observer to tell the difference whether the charge is located in the core of the black hole, or on the event horizon? The quantum explanation (what you linked) seems to be saying, in short, that "the EM field can pass the event horizon because the virtual particles conveying the force, can pass the event horizon" which doesn't really solve the problem, just introduces some new particles with peculiar properties.

I don't understand your concern? You are almost speaking of the E-field as if it were in motion when you say something like why the EM field can escape. Why does that bother you and not the fact that the gravitational field itself can "escape" from the black hole?

Pete

 

[ehj]

I don't understand your concern? You are almost speaking of the E-field as if it were in motion when you say something like why the EM field can escape. Why does that bother you and not the fact that the gravitational field itself can "escape" from the black hole?

Pete

The gravitational "field" is the curvature of spacetime and not an actual field like the EM field, that's how it "escapes" the black hole. My concern is the fact that from within the event horizon of a black hole there exists no path through spacetime leading out of the black hole - atleast not for anything with mass or energy. But then someone says that the EM field has a mass, and if nothing with mass can leave the black hole, then how can the charge me measured from the outside? The field having mass makes me think of it as consisting of something that can be attracted or bent by gravity - is this not correct?

 

[pmb_phy]

The gravitational "field" is the curvature of spacetime ..

That is incorrect. The presence of a gravitational field does not require the presence of spacetime curvature. The term spacetime curvature is merely a term which refers to tidal forces. Its use does not mean that there is no field. In any case what makes you think that the spacetime outside the event horizon can know that there is mass inside the event horizon and "know" to curve spacetime?

My concern is the fact that from within the event horizon of a black hole there exists no path through spacetime leading out of the black hole - atleast not for anything with mass or energy.

All that means is that there can be nothing which moves from the inside to the outside the event horizon. The electric field doesn't move nor is there a flow of energy associated with it.

But then someone says that the EM field has a mass, ..

Yes. It does.

...and if nothing with mass can leave the black hole, then how can the charge me measured from the outside?

Once again, there is nothing leaving the black hole. The field is static as is the distribution of matter. There is no flow of energy either into or out from the event horizon.

The field having mass makes me think of it as consisting of something that can be attracted or bent by gravity - is this not correct?

Fields contain not only energy but also stress and tension. The tension acts to reduce the mass in certain instances. Perhaps this is why the matter of the field is not attracted by the field. In a certain sense the mass density of the field is zero, even though the energy density isn't. This is one of those less known facts about relativity.

Pete

 

[ehj]

Thanks, now it makes sense :)

 

[gendou2]

That is incorrect. Light most certainly does generate a gravitational field. Take a look at the second link that you posted because it says

Why would you believe otherwise??

What you call an equivalent mass is what is known as inertial mass aka relativistic mass.

When you state it that way it gives the impression that "equivalenc" mass is somehow different that the "real" mass (whatever "real" means)

Notice that your second link contains the following comment.

Before one addresses the question regarding whether a photon/light has mass or not you really must state what definition you are using. A photon has an inertial mass (since it has momentum) a passive gravitational mass (since it is affected by gravity) and an active gravitational mass (since it can generate a gravtiational field).

Pete

Thanks for correcting me on my many mistakes. I was unaware that photons have gravitational fields! I thought it was the rest mass that caused gravitational fields. Can you show me how photon gravity is predicted, mathematically?

 

[pmb_phy]

Thanks for correcting me on my many mistakes. I was unaware that photons have gravitational fields! I thought it was the rest mass that caused gravitational fields. Can you show me how photon gravity is predicted, mathematically?

Sure. I worked this out for a beam of light (or rather I followed the derivation). I sent you the link to the math.

Pete