Adding a huge electric charge to a black hole?

[Go Nucelar]

I wonder, what would happen if you started dropping lots of electrons into an existing black hole which otherwise doesn't accrete any new matter?

The charge of the black hole would build up much faster than the mass. Wouldn't its charge become so high at one point that further electrons would no longer fall through the event horizon due to the electromagnetic repulsion?

Can this process be used to even "deconstruct" a black hole, by charging it to a point where it would simply explode?

 

[Grinkle]

Since its a B thread, I will hazard a response. Electric force is transmitted by particles. No particles can escape the black hole, so it does not accumulate negative electric charge that is felt outside the event horizon as you are supposing.

 

[Drakkith]

From the perspective of an outside observer, the electrons never pass the event horizon because of time dilation (or something like that. It's complicated once you factor in Hawking radiation and evaporating black holes). This means that their charge does build up over time.

The charge of the black hole would build up much faster than the mass. Wouldn't its charge become so high at one point that further electrons would no longer fall through the event horizon due to the electromagnetic repulsion?

I believe that's correct.

Can this process be used to even "deconstruct" a black hole, by charging it to a point where it would simply explode?

It cannot.

 

[Grinkle]

I retract my response.

@Drakkith

Since this is true -

From the perspective of an outside observer, the electrons never pass the event horizon

for what observer does this statement apply?

at one point that further electrons would no longer fall through the event horizon

 

[Drakkith]

for what observer does this statement apply?

Ignoring evaporation, any observer that never passes the event horizon. For example, an observer many light-years away, or even one hovering several radii outside the event horizon. But it wouldn't be the same for an in-falling observer, one who is in free fall towards the event horizon. As far as I know at least. I'm not an expert on black holes so I may have some details wrong.

 

[stefan r]

"dropping" an electron would not work if the repulsion from charge exceeds the attraction from gravity. You would have to accelerate the electrons and shoot them at the black hole. The accelerated electrons have more energy than a non-accelerated electron. Adding energy to a black hole is equivalent to adding mass to the black hole.

...the electrons never pass the event horizon because of time dilation (or something like that...

I believe time dilation prevents them from reaching the singularity. Since we are pumping "enough" energy into the black hole the event horizon will expand and electrons will be inside of it.

 

[Drakkith]

I believe time dilation prevents them from reaching the singularity.

Not as far as I understand things. To the best of my knowledge time dilation and redshift approach infinity as you near the event horizon, as seen from the reference frame of an observer who is well away from the black hole.

 

[stefan r]

Not as far as I understand things. To the best of my knowledge time dilation and redshift approach infinity as you near the event horizon, as seen from the reference frame of an observer who is well away from the black hole.

Take for example a type II supernova event. It looked like there was a big star there yesterday, now it looks like there is a black hole. Yesterday there was no event horizon, now there is one and it is outside of/around the particles. Light emitted by a former-inner-star particle will never get here. A photon emitted by a particle slightly outside the event horizon today will not get here for a long time and it will be red shifted if it does. The core collapse did happen this morning. Background radiation orbited a black hole and is on its way here. Yesterday background radiation bent but it could not orbit. There is "stuff" inside an event horizon today and that "stuff" was not inside an event horizon yesterday.

 

[Drakkith]

Take for example a type II supernova event. It looked like there was a big star there yesterday, now it looks like there is a black hole. Yesterday there was no event horizon, now there is one and it is outside of/around the particles. Light emitted by a former-inner-star particle will never get here. A photon emitted by a particle slightly outside the event horizon today will not get here for a long time and it will be red shifted if it does. The core collapse did happen this morning. Background radiation orbited a black hole and is on its way here. Yesterday background radiation bent but it could not orbit. There is "stuff" inside an event horizon today and that "stuff" was not inside an event horizon yesterday.

According to Paul Townsend there is an infinite amount of time dilation at the horizon, not the singularity. From page 125 at this link: http://xxx.lanl.gov/pdf/gr-qc/9707012v1

The spacetime associated to gravitational collapse to a black hole cannot be everywhere stationary so we expect particle creation. But the exterior spacetime is stationary at late times, so we might expect particle creation to be just a transient phenomenon determined by details of the collapse. But the infinite time dilation at the horizon of a black hole means that particles created in the collapse can take arbitrarily long to escape - suggests a possible flux of particles at late times that is due to the existence of the horizon and independent of the details of the collapse. There is such a particle flux, and it turns out to be thermal - this is Hawking radiation

 

[stefan r]

According to Paul Townsend there is an infinite amount of time dilation at the horizon, not the singularity. From page 125 at this link: http://xxx.lanl.gov/pdf/gr-qc/9707012v1

Great link. thanks.
I do not see a contradiction.
Suppose we threw a very bright clock into a black hole. We knew where the black hole was and we knew the velocity and acceleration on the clock. We tossed at 12:00 and it should be in the hole at 12:10. Later (hours, or years) we look through a powerful telescope and detect photons radiating from just outside the event horizon. The clock display will show less than 12:10. These photons were emitted before the clock went into the hole. This observation does not change the location of the clock. Instead this is evidence that the clock was on the way in. It has arrived there. The clock is inside the event horizon.

 

[Drakkith]

The clock display will show less than 12:10. These photons were emitted before the clock went into the hole. This observation does not change the location of the clock. Instead this is evidence that the clock was on the way in. It has arrived there. The clock is inside the event horizon.

I don't think so. If there is indeed an infinite amount of time dilation at the event horizon, then the clock is not inside the event horizon yet. And never will be from our frame of reference.

 

[triclon]

Things in space tend to be electrically neutral and there is a good reason for that. If you dumped electrons in a black hole to give it a large negative charge, you might be able to repel other electrons but positively charged particles (e.g. protons) would experience an even greater attractive force towards the black hole and the hole would quickly become electrically neutral as it pulled in surrounding positively charged matter.

 

[snorkack]

How much charge can a Nordström black hole have?

 

[SlowThinker]

How much charge can a Nordström black hole have?

In many paper the authors say that max Q=M, however they don't bother to specify units. When I asked about it earlier, @PeterDonis said to use Geometrized Units. Unless I made a mistake, a solar mass black hole would hold some 1.15 10^17 C.

 

[snorkack]

How does the mass/charge ratio of a Nordström hole compare against an electron?

 

[SlowThinker]

How does the mass/charge ratio of a Nordström hole compare against an electron?

That is something you can find out.

 

[phinds]

Things in space tend to be electrically neutral and there is a good reason for that. If you dumped electrons in a black hole to give it a large negative charge, you might be able to repel other electrons but positively charged particles (e.g. protons) would experience an even greater attractive force towards the black hole and the hole would quickly become electrically neutral as it pulled in surrounding positively charged matter.

That assumes that there IS "surrounding positively charged matter". Why would you make such an assumption?

 

[snorkack]

That is something you can find out.

A mole of electrons weighs about 0,55 mg, and has a charge of 96 485 coulombs.
The amount of 1,15*10¹⁷ C should be something like 1,2*10¹² moles of electrons... weighing a mere 650 tons.

 

[ivant6900]

Actually nothing would happen at all.
First you need to consider the origin of an electron and how it gets its mass, where it gets its mass from. Also it is important to remember that mass equal energy.
So electron gets its mass from the Higgs field and for that to happen something called "spontaneous symmetry" has to break down. However we know that it can be restored in high energy fields which means that once the electron passes through the Event Horizon and heads down towards the singularity it loses its mass and essentially seizes to exist as an electron...there is no charge transfer at all...

 

[phinds]

Actually nothing would happen at all.
First you need to consider the origin of an electron and how it gets its mass, where it gets its mass from. Also it is important to remember that mass equal energy.
So electron gets its mass from the Higgs field and for that to happen something called "spontaneous symmetry" has to break down. However we know that it can be restored in high energy fields which means that once the electron passes through the Event Horizon and heads down towards the singularity it loses its mass and essentially seizes to exist as an electron...there is no charge transfer at all...

Then how do you explain that all the black hole experts say that charge is one of the fundamental properties of a black hole?

 

[ivant6900]

Then how do you explain that all the black hole experts say that charge is one of the fundamental properties of a black hole?

I would challenge you to demonstrate such claim with reference links because I know for a fact that electron or any other particle for that matter cannot exist under such conditions and that the closer you get to the singularity the less regular physics applies and the more gravitational and string theory applies...

 

[Drakkith]

However we know that it can be restored in high energy fields which means that once the electron passes through the Event Horizon and heads down towards the singularity it loses its mass and essentially seizes to exist as an electron...there is no charge transfer at all...

I know for a fact that electron or any other particle for that matter cannot exist under such conditions and that the closer you get to the singularity the less regular physics applies and the more gravitational and string theory applies...

Please provide a valid reference for these claims.

 

[ivant6900]

If you need reference please see the Higgs Field principle and electron mass creation and destruction, General systems approach to symmetry principles of the Unified Field Theory as well as the Quantum Gravity and String Theory for the singularity of a black hole...

 

[SlowThinker]

once the electron passes through the Event Horizon and heads down towards the singularity it loses its mass and essentially seizes to exist as an electron...there is no charge transfer at all...

What happens under the event horizon is irrelevant to outside observer, who is the one measuring the black hole's charge.

 

[JLowe]

I don't think so. If there is indeed an infinite amount of time dilation at the event horizon, then the clock is not inside the event horizon yet. And never will be from our frame of reference.

But does the black hole's mass never increase from our frame of reference? If we measure a change in mass of the black hole, and an expanding horizon, is it not valid to say we've witnessed matter falling into the horizon?

 

[nikkkom]

So electron gets its mass from the Higgs field and for that to happen something called "spontaneous symmetry" has to break down. However we know that it can be restored in high energy fields which means that once the electron passes through the Event Horizon and heads down towards the singularity it loses its mass and essentially seizes to exist as an electron...there is no charge transfer at all...

Even if you are right about EW symmetry restoration happening inside BH and also that this affects it exterior (I suspect both are not true), restoration of EW symmetry does not "destroy" the notion of electric charge.

If anything, it restores conservation of weak hypercharge and weak isospin, and electric charge is a simple linear combination of these two. Thus, Q will continue to be conserved.

 

[phinds]

I would challenge you to demonstrate such claim with reference links because I know for a fact that electron or any other particle for that matter cannot exist under such conditions and that the closer you get to the singularity the less regular physics applies and the more gravitational and string theory applies...

You would do well to read some basic cosmology

https://en.wikipedia.org/wiki/No-hair_theorem

EDIT: Wikipedia is not, in general, a great reference for PF but the no hair theorem is so well known that I think it's OK in this case.

 

[Drakkith]

If you need reference please see the Higgs Field principle and electron mass creation and destruction, General systems approach to symmetry principles of the Unified Field Theory as well as the Quantum Gravity and String Theory for the singularity of a black hole...

Once again, please provide a valid reference for your claim that charge is destroyed and not "transferred" to the black hole when an electron falls into it. Saying "see these 4 things" does not count as a valid reference. Especially since there is no accepted theory of quantum gravity.

But does the black hole's mass never increase from our frame of reference? If we measure a change in mass of the black hole, and an expanding horizon, is it not valid to say we've witnessed matter falling into the horizon?

The mass inside some radius from the center of the black hole increases as stuff falls towards the black hole, regardless of whether it has already passed the event horizon. So even though a particle may still be outside the EH, its mass still counts (as an approximation of course) unless your're closer to the black hole than the particle. My understanding is that as particles fall towards the EH, they become unobservable as the light from them is redshifted outside of our capabilities of detection, leading to a situation that could be described as "they might as well be inside the EH".

 

[JLowe]

The mass inside some radius from the center of the black hole increases as stuff falls towards the black hole, regardless of whether it has already passed the event horizon. So even though a particle may still be outside the EH, its mass still counts (as an approximation of course) unless your're closer to the black hole than the particle. My understanding is that as particles fall towards the EH, they become unobservable as the light from them is redshifted outside of our capabilities of detection, leading to a situation that could be described as "they might as well be inside the EH".

I guess what I'm asking is how an outside observer can ever detect the horizon of a black hole increase in radius if we are never able to witness anything fall beyond the original event horizon. At some point, couldn't the number of redshifted particles at the horizon be so massive that from our perspective the infalling matter has its own horizon, with radius larger than the spot we last detected the redshifted particles.

 

[Drakkith]

I guess what I'm asking is how an outside observer can ever detect the horizon of a black hole increase in radius if we are never able to witness anything fall beyond the original event horizon. At some point, couldn't the number of redshifted particles at the horizon be so massive that from our perspective the infalling matter has its own horizon, with radius larger than the spot we last detected the redshifted particles.

That I can't answer. I'm afraid we may have reached the limits of my knowledge in this area.

 

[mfb]

@Drakkith and @JLowe: For all practical purposes, matter does fall in. If you let a light source fall in and calculate the expected intensity an observer far away will receive, this intensity never reaches zero - but it goes down exponentially with a short time constant. You will quickly receive the last photon you will ever get from this object. Afterwards you can calculate that it could still be 10^-100 m away from the event horizon, but that doesn't make sense - it is an artifact of a poor choice of units that diverge at the event horizon. Choose different time units and the object does fall in.

However we know that it can be restored in high energy fields which means that once the electron passes through the Event Horizon and heads down towards the singularity it loses its mass and essentially seizes to exist as an electron...there is no charge transfer at all...

It does not lose its mass, and it does not lose its charge either. Locally you don't even notice the gravitational field, one of the fundamental principles of general relativity.

Black holes can be charged, the corresponding metric has been found by Reissner and Nordström. Charge is conserved - if you shoot charged objects at a black hole, the black hole changes its charge accordingly.

Reissner, H. (1916). "Über die Eigengravitation des elektrischen Feldes nach der Einsteinschen Theorie". Annalen der Physik 50: 106–120
Nordström, G. (1918). "On the Energy of the Gravitational Field in Einstein's Theory". Verhandl. Koninkl. Ned. Akad. Wetenschap., Afdel. Natuurk., Amsterdam. 26: 1201–1208.Coming back to the original question: A black hole has a maximal charge, as discussed in post 14 already. At this maximal charge, electrostatic repulsion will be stronger than gravitational attraction for charged particles. You have to actively shoot them towards the black hole - adding so much energy that both the mass of the black hole increases enough to increase its charge as well.
The conversion factor is ##(G 4 \pi \epsilon_0)^{1/2} = 8.6 \cdot 10^{-11} C/kg = 5 \cdot 10^{-22} e/m_e = e/(2µg)## where e is the elementary charge and m_e is the electron mass.
We have to give the electron (or proton, or any other singly charged particle) ) the energy equivalent to 2µg of mass to get into the maximally charged black hole, assuming it has the same charge as our electron (proton/...).

Spoiler: beyond [B

level]You might recognize the combination of gravitational constant and 4 pi eps_0. The Planck mass and the fine-structure constants have similar combinations,, and the 2µg from above turn out to be ##\sqrt{\alpha}## times the Planck mass with the fine-structure constant ##\alpha##.

 

[Ilythiiri]

Thread is not closed, so (:
Among fuzzy questions about BH's, most frustrating for me is charge part.

Coming back to the original question: A black hole has a maximal charge, as discussed in post 14 already. At this maximal charge, electrostatic repulsion will be stronger than gravitational attraction for charged particles.

Wiki: "...Magnetism is a class of physical phenomena that are mediated by magnetic fields. ...", "...The electromagnetic force, carried by the photon, creates electric and magnetic fields, which are..."

Electromagnetic interaction is cut at event horizon. In what way charge property can be useful in predicting BH behaviour? How can BH charge be measured, even if hypothetically, if there's no force carrier?

There's this link from another discussion:
http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/black_gravity.html
"... 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. ..."

This sounds like measurement of BH ergosphere's charge.

"... 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..."

So, charge is mediated by Hawking radiation? This sounds ... hairy to me.

 

[mfb]

Electromagnetic interaction is cut at event horizon.

The electromagnetic field of charged black holes can be described by looking at the outside only - similar to the gravitational influence.

How can BH charge be measured, even if hypothetically, if there's no force carrier?

By looking at the force on test charges, like everywhere else.

So, charge is mediated by Hawking radiation?

No, and Baez doesn't claim that.

Keep in mind that virtual particles are a mathematical tool - they are not real.

 

[Ilythiiri]

I browsed through related discussions. So ...

I think the biggest misconception about black holes is that physicists agree on what they are. I know of no example of mainstream physics literature where the experts in the field disagree more completely than on the topic of what goes on inside an event horizon.

... yeah.

Okay then, my misunderstanding was that only object inside event horizon is considered BH.

Read up about https://en.wikipedia.org/wiki/Membrane_paradigm and https://en.wikipedia.org/wiki/Magnetospheric_eternally_collapsing_object
Less fuzzy now.

Keep in mind that virtual particles are a mathematical tool - they are not real.

Yes I've read PF series on that, some illusions broke there (: That's what i meant by "hairy".

 

[256bits]

Keep in mind that virtual particles are a mathematical tool - they are not real.

Is this just a PF thing, as a lot of references say they are in fact real , for example explaining the Lamb shift, Casmir effect, Black Hole evaporation ( not the two particle idea - one being trapped inside, the other not ). The vacuum energy does need and explanation, and the fields of space and fluctuations would have to be mathematical tools themselves.
Here is one person who says they are real.
https://www.scientificamerican.com/article/are-virtual-particles-rea/

Gordon Kane, director of the Michigan Center for Theoretical Physics at the University of Michigan at Ann Arbor, provides this answer.

Virtual particles are indeed real particles. Quantum theory predicts that every particle spends some time as a combination of other particles in all possible ways. These predictions are very well understood and tested.