B Adding a huge electric charge to a black hole?

[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.

 

[mfb]

You can derive the Lamb shift and the Casimir effect without virtual particles (example). The mathematics of Hawking radiation has nothing that could be interpreted as virtual particles - this is purely a pop-science myth.

Does the number 3 exist as physical object? Clearly not - it is a mathematical tool. Same for virtual particles. If you think virtual particles are physical objects, then the number 3 should be a physical object as well. I think that is a very strange view.

 

[256bits]

Number 3 may not be physical, but it certainly is real.
Virtual particles are not physical, but are they real?
That's why I am wondering if it is a PF thing, or a general physics thing, in an attempt to de-evaluate the concept.
Perhaps, until better mathematical tools come about that do not produce such an artifact, virtual particles are here to stay.

PS.
You definitely misinterpreted the use of my word "thing". I should not be so colloquial.

 

[DaveC426913]

Perhaps, until better mathematical tools come about that do not produce such an artifact, virtual particles are here to stay.

I think they are a shortcut.
Rigorously, the math can be done without them, but it is much more complex.

Likewise: Some electrical equations are defined and solved using imaginary numbers, because they are a useful tool. But the equations can be done without them, they're just much harder. The imaginary numbers do not represent any real counterpart in the phenomenon itself.

Caveat: I do not speak with any authority on this.

 

[phinds]

Virtual particles are not physical, but are they real?

What do you think is the distinction between "physical" and "real". Do you think virtual particles are like love or hate?

 

[256bits]

Caveat: I do not speak with any authority on this.

Same here.
It's the chosen word that sows confusion I believe.
Kind of like virtual image - not a real image, but an image nevertheless.
By that analogy, virtual particles should be not a real particle but a still particle.
Imaginary might have been more palatable for understanding at the outset.

Physics does have its problems with descriptive terms.
Black hole was objected to due to the obvious connotations for some, but the name stuck.

 

[256bits]

What do you think is the distinction between "physical" and "real". Do you think virtual particles are like love or hate?

See the above post - virtual image.

 

[Chronos]

Dealing with the kinowns - a black hole is believed to have 3 intrinsic properties a] mass b] angulatr momentum c] charge. Our experience with nature suggests these properties have a maximal finite limit.. In the case of a black hole, calculations suggest the area of the event horizon dictates the maximal limit of its intrinsic properties. So it follows the area of the event horizon must increase to accommodate an increase in the value of any intrinsic property beyond its maximal limit.. It's like trying to stuff 10 pounds of crap into a 5 lb sack. Either the sack expands or you get a pile of crap on the floor.

 

[mfb]

Number 3 may not be physical, but it certainly is real.

It is a "real number" in mathematics, but I wouldn't assign it any "physical reality". Pick 3+2i if you like that comparison more.
Anyway, this is getting philosophical.