# Will charged black holes evaporate?

1. Apr 20, 2012

### Tachyonguy

Black holes only emit hawking radiation which is black body radiation. If black holes only emit photons then the black hole can never get rid of charge which means it can never get rid of all its mass. Does this means black holes also emit charged particles?

2. Apr 20, 2012

### phinds

What makes you think black holes only emit photons? I have never heard that before.

3. Apr 20, 2012

### Drakkith

Staff Emeritus
I've never heard otherwise actually. How could any virtual particles other than photons created outside the event horizon get enough velocity to escape the BH's gravity?

4. Apr 20, 2012

### phinds

Good point. My problem is that I have a very mild dyslexia and while both the OP and I used the word "photon", my brain was processing, in both cases, the word "proton". Thanks for that correction.

Last edited: Apr 20, 2012
5. Apr 20, 2012

Staff Emeritus
You get a thermal spectrum of all particles. Of course, with T < 1 MeV you cannot make electrons.

6. Apr 21, 2012

### Tachyonguy

7. Apr 21, 2012

### Staff: Mentor

Blackbody radiation is electromagnetic radiation at "low" temperatures. Here, even our fusion reactors have "low" temperatures of some keV. Small black holes can have temperatures above ~500keV, where electrons and positrons join the blackbody spectrum in significant amounts.

If the charge is very large, the energy threshold for one of the charges is lower, which can lead to electron or positron emission (depending on the sign of the charge) at lower temperatures, too.

With even higher temperatures (~100MeV), muons and pions join the blackbody spectrum, and so on.
Neutrinos should be part of the spectrum, too, but probably really rare as they have to be produced via the weak interaction.

Oh, and one important thing for real black holes: If they are charged, they quickly accumulate the opposite charge, as the electromagnetic interaction is much stronger than gravity. This leads to the idea that existing cosmic black holes are nearly uncharged.

8. Apr 23, 2012

### Chronos

Charge is offset by the negative energy of the gravitational field of a black hole. So that is a big zero net effect.

9. Apr 18, 2013

### Trenton

Evaporation is a slow process but I am wondering if a charged black hole can undergo a different process - that of complete singularity disruption.

The charged black hole, according to a number of articles on the subject, has the singularity at the center of course but also an inner horizon in addition to the outer gravitational one. I am more than a little troubled by this model.

Although it is meaningless to speak of space moving, for want of a better term, the outer horizon forms because the gravitational potential creates a situation which equates to space 'falling' at the newtonian escape velocity. This is c at the horizon and >c inside. Any outbound photon at the horizon swims upstream and goes nowhere. Inside the photon swims upstream but is overhwelmed and swept backwards by the virtual 'current'.

If anyone can improve on the above horrible description please do!

At the inner horizon though, the 'stream' slows to a halt (according to the articles) - but I don't see this as viable. One could envisage a cloud of electrons or protons sat outside the singularity because the electrostatic repulsion balanced gravity but what of uncharged infalling matter? Relative to one another, charged particles and uncharged particles would violate the speed of light.

It is better to place the net charge inside the singularity and lose the inner horizon. Of course the nature of a singularity is conjecture but one theory is that all the matter is converted to bosons (as this gets round the pauli exclusion principle). If this is the case all the bosons in an uncharged and unspinning singularity would occupy the same point in space and would all point outwards. They would be held in by the 'infall' of space. In a charged singularity bosons would form a hollow sphere in much the same way as they form a ring in a spinning singularity. The singularity is the inner horizon if you like.

An extremal charged black hole is defined as one in which the inner horizon equals the outer one. It is thought that the inner electrical horizon cannot exceed the outer gravitational one as this would render the singularity naked. Separately it has been suggested that in practice, a black hole could never aquire enough charge to become extreamal.

I would describe this differently. With the charge lying inside the hollow sphere of bosons, it can build to the point where the radius becomes equal. But the instant the boson sphere exceeds the EH the bosons are free to leave.

No violation of cosmic censorship. Just a very good candidate for ultra short duration gamma ray burst.

10. Apr 18, 2013

### Mordred

I'm not sure if this will apply in this case but what about Schwinger particle pair production. Which involves electric fields?

11. Apr 18, 2013

### Trenton

I am not sure I understand what you are asking? Are you considering what is happening to pairs of fermions before they cancel each other out within the context of a hollow spherical singularity of bosons or within any other context?

12. Apr 18, 2013

### Mordred

My knowledge on Shwinger is sketchy at best. I studied Hawking, Unruh and Parker particle production as well as false vacuum.
Anyways Shwinger is if I understand correctly applied to uniform electric fields. Ive read technical articles where its applied to magnetars. So Im wondering if its been applied to a BH.? Or can it be?
Every paper Ive read has either been Hawking or Unruh.
In regards to a BH.
By the way I would greatly appreciate good articles on Schwinger in regards to other Cosmology usages.

13. Apr 19, 2013

### Mordred

I had to check the article I had previously gathered. As I previously stated I'm not too familiar with it been reading too many other articles lol.
To answer you Trenton yes I do mean fermion boson production.
Heres the article.

http://arxiv.org/abs/1208.0478

Could this not apply to the accretion disk.? If or if not the EH?

14. Apr 19, 2013

### Staff: Mentor

An extremal black hole requires 2rQ=rs, or $\frac{Q^2G}{\pi \epsilon_0 c^4} = \frac{4G^2M^2}{c^4}$. This can be simplified to $Q^2=4\pi \epsilon_0 GM^2$.

A naive calculation of the electric field strength at the event horizon rs/2 gives $E=\frac{Q}{\pi \epsilon_0 r_s^2} = \frac{Qc^4}{4\pi \epsilon_0 G^2M^2} = \frac{c^4}{GQ}$.
To get below 1016V/cm, we need a charge of more than 1028C, corresponding to 70 million solar masses (1.4*1038kg) for an extremal black hole. This will not happen :D.

15. Apr 19, 2013

### Mordred

Thank you so very much. That definetely answered all my Schwinger mechanism questions in regards to a BH.
Now I understand why I only see its application on magnetars as well.

Lol you have no idea how long that question was bugging me.

Last edited: Apr 19, 2013
16. Apr 20, 2013

### Trenton

Replying to mfb, I had been working on the basis that the electrostatic charge would only need to counteract gravity. For a solar mass BH this would be 1.5 trillion g and charge of 15 billion C. This is the sort of charge that a nuclear powered ion engine could concievably deliver, let alone matter acreating onto a magnetar. But to be honest I don't know if couteracting gravity is enough. I don't know about the Q2=4πϵ0GM2. formula.

But the question of if a black hole can be blown apart by charging it was only an eye-catching bit of drama on my part. More seriously, there appears to be a flaw in the idea of an inner horizon for a charged BH regardless of whether the mass of the BH remains concentrated at the center or exists in a hollow shpere with the electrons residing in the zero gravity region within. Both models have the radius of either the inner horizon or sphere increasing with increasing charge - this is what can't happen. Not only can nothing be at rest between the EH and the singuarity, it must be moving inwards.

As for a charged BH counteracting being charged by some sort of variation of pair production, I am not sure how this would happen. Can pair production be selective in this way?

17. Apr 20, 2013

### Staff: Mentor

Pair production close to a black hole (but outside), if electrostatic forces are stronger than gravity, will certainly lead to a charge reduction of the black hole - a negatively charged black hole will "emit" electrons in that way, and a positively charged black hole will emit positrons.

18. Apr 20, 2013

### Trenton

Good point, pair production outside would reduce the charge, provided of course that the electrostatic field could be felt outside the EH. Of the 3 quantities of mass, spin and charge, it is clear how the first two could be manefest to an outside observer, less so the latter. What is the prevailing view on this? Can charge be felt outside and if so by what mechanism? If it can a BH won't be charged for long but if it can't until the electrostatic force equals or exceeds gravity, then this it will be too late for the BH, it would beome a gamma ray burst.

The 'virtual stream' model I spoke of earlier, in which there is an apparent equivilence to space falling at the newtonian escape velocity, would appear to rule out any possibility of charge being felt outside the singularity, let alone the EH.

Again I must ask though, does anyone have a better description than the space falling thing? I am stuck with it for now but it does make me wince!

19. Apr 20, 2013

### Mordred

Not sure if this will help you but there is a section dealing with magnetized tori in this blackhole accretion disk compilation.
Essentially its a collection of formulas related to measuring aspects of the accretion disk and jets.
The charge aspect outside the EH made me remember that section

http://arxiv.org/abs/1104.5499

20. Apr 21, 2013

### yenchin

Look at the second post and the links therein at http://physics.stackexchange.com/questions/12169/detection-of-the-electric-charge-of-a-black-hole.