Will charged black holes evaporate?

[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?

 

[phinds]

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

 

[Drakkith]

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

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?

 

[phinds]

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?

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.

 

[Vanadium 50]

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

 

[Tachyonguy]

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

I have read on wikipedia that hawking radiation is black body radiation which is electromagnetic radiation.

 

[mfb]

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.

 

[Chronos]

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

 

[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 acquire 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.

 

[Mordred]

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

 

[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?

 

[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. I've read technical articles where its applied to magnetars. So I am wondering if its been applied to a BH.? Or can it be?
Every paper I've 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.

 

[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?

 

[mfb]

An extremal black hole requires 2r_Q=r_s, 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 r_s/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.

 

[Mordred]

Thank you so very much. That definitely 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.

 

[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?

 

[mfb]

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.

 

[Trenton]

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.

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!

 

[Mordred]

Not sure if this will help you but there is a section dealing with magnetized tori in this black hole 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

 

[yenchin]

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?

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.

 

[Mordred]

This is a quote from the article I posted. Its related as they go into decent details on how energy is carried away by yhe accretion disk/jets.
The article also goes indepth on the electrmagnetic properties.

Magnetic fields may play many interesting roles in black hole accretiondisks. Largescale magnetic fields threading a disk may exert a torque,thereby extracting angular momentum[48].Similarly, large scale poloidal magnetic fields threading the innerdisk,ergosphere,or black hole,have been shown to be able to carry energy and angular momentum away from the system,and powerjets[49]. Weak magnetic fields can tap the differential rotation of the disk itself to amplify andtrigger an instability that leads to turbulence, angular momentum transport, and energy dissipation(exactly the processes that are needed for accretion to happen)[26,27]. In most black hole accretion disks,it is reasonable to assume ideal MHD, where by the conductivity is infinite, and consequently the magnetic diffusivity is zero. Whenever this is true,magnetic field lines are effectively frozen into the fluid. A corollary to this is that parcels of fluid are restricted to moving along fieldlines, like“beads”on a wire.In ideal MHD, the Faraday tensor obeys the homogeneous Maxwell’s equation µ(∗Fµν)=0, (67

 

[Mordred]

Later on in the article it discusses a condition where the magnetic field lines can halt the fall of inflowing material granted they specify that's its shown in simulations

examples are interesting because they have led directly to a phenomenon known as a“magnetically arrested” accretion state[218],where the accumulation of magnetic field near the black hole is strong enough to stop the flow of infalling material

 

[Trenton]

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.

This article seems only to deal with a black hole that was formed with an initial charge? I was wondering what would happen if a beam of either protons or electrons were to be directed at a black hole. I don't think the strengthening electrostatic field inside the hole would be able to climb outwards at all, let alone reach and then escape the EH. As I understand it, inside the EH an outgoing photon is 'blown backwards' toward the center. Surely this must happen also to an electric field?

 

[Mordred]

The radiation pressure (including electromagnetic) can build up enough to counter gravity of a BH. See the reference article for details on the magnetically arrested section I posted above. Although its outside the EH it does describe a characteristic wher infalling material can be halted rather than blown back.