Evaporating black holes and conservation of charges?

[Suekdccia]

TL;DR Summary

Will evaporating black holes (with neutral charge) emit the same amount of electrons and positrons to conserve charge when their Hawking temperature is high enough? What about charged black holes?

Black holes are expected to evaporate due to Hawking Radiation [1]. As they would lose mass with this process, their radius would also shrink. According to Hawking temperature [2], since it is inversely proportional to the mass of the black hole, as the radius (or the mass) decreases, the black hole would be able to radiate more energetic electromagnetic radiation. Following this, there will be a moment where they should be able to radiate massive particles. One example of a massive parricle that they could emit is the electron.

However, if they would conserve charge, wouldn't they have to emit at the same moment a positron? Or this emission is random and therefore a black hole could emit more electrons than positrons (and vice versa)? What about charged black holes?

[1]: https://en.wikipedia.org/wiki/Hawking_radiation

[2]: https://commons.wikimedia.org/wiki/File:Formula_for_blackbody_temperature_of_Hawking_radiation.png

 

[mitchell porter]

The black hole itself has charge, which changes when charged particles are emitted.

 

[Suekdccia]

The black hole itself has charge, which changes when charged particles are emitted.

Aren't there neutral black holes?

 

[mitchell porter]

Aren't there neutral black holes?

If a neutral object emits a positive charge, it acquires a negative charge itself, to maintain charge conservation.

 

[Suekdccia]

If a neutral object emits a positive charge, it acquires a negative charge itself, to maintain charge conservation.

Alright

So then, can black holes emit electrons randomly without emitting positrons (after having their radius and mass very reduced) at the cost of acquiring positive charge?

 

[Demystifier]

Alright

So then, can black holes emit electrons randomly without emitting positrons (after having their radius and mass very reduced) at the cost of acquiring positive charge?

Yes.

 

[Suekdccia]

Yes.

Okay

And once they acquire positive charge they will start to emit positrons? Or not necessarily?

Also, then, if instead of a neutral black hole we would have a charged black hole from the beginning, would they lose charge by emitting opposite charged particles before reaching the size to be able to produce massive particles? Or it would be the same case as this one we're discussing?

 

[mitchell porter]

Whether a black hole is electrically neutral, negative, or positive, its Hawking radiation can contain particles with any charge, and the black hole's own charge will adjust to maintain charge conservation. The one likely limit on this, is if the black hole reaches an "extremal" state. This is a boundary on mass, spin, and charge, beyond which the event horizon would disappear, leaving a naked singularity. This is generally thought to be impossible (and in string theory, at least, there are calculations suggesting that it is prevented from happening), so we may posit that the one restriction on charged Hawking radiation, is that it will not be allowed if it would leave the black hole in a super-extremal state.

Of course, Hawking radiation has never been observed, so there's no empirical evidence that this is how black holes actually work; like the whole concept of Hawking radiation, these are deductions from physical principles.

 

[Demystifier]

And once they acquire positive charge they will start to emit positrons? Or not necessarily?

Not necessarily.

 

[Suekdccia]

Whether a black hole is electrically neutral, negative, or positive, its Hawking radiation can contain particles with any charge, and the black hole's own charge will adjust to maintain charge conservation. The one likely limit on this, is if the black hole reaches an "extremal" state. This is a boundary on mass, spin, and charge, beyond which the event horizon would disappear, leaving a naked singularity. This is generally thought to be impossible (and in string theory, at least, there are calculations suggesting that it is prevented from happening), so we may posit that the one restriction on charged Hawking radiation, is that it will not be allowed if it would leave the black hole in a super-extremal state.

Of course, Hawking radiation has never been observed, so there's no empirical evidence that this is how black holes actually work; like the whole concept of Hawking radiation, these are deductions from physical principles.

So basically the type of particle that a black holes radiates is really random?

 

[WWGD]

If a neutral object emits a positive charge, it acquires a negative charge itself, to maintain charge conservation.

Is this a Statistical, or literal/Mathematical property, i.e. , must it hold at all times, or is it true a large percent of the time?

 

[Nugatory]

So basically the type of particle that a black holes radiates is really random?

As far as we know, but we do not have a complete theory of quantum gravity. So everything you’ll read about black hole radiation includes some assumptions that may not hold up over time.

 

[mitchell porter]

Is this a Statistical, or literal/Mathematical property, i.e. , must it hold at all times, or is it true a large percent of the time?

Charge will be conserved in any individual event. The randomness (in quantum mechanics) lies in which events actually happen, but charge is conserved in each case.

So basically the type of particle that a black holes radiates is really random?

Not only that, but the debate around the "black hole information paradox" was originally about whether the randomness involved is just ordinary quantum randomness, or something more, that would even involve the forgetting of wavefunction information.

In ordinary quantum randomness, what happens may be random, but the probabilities at least depend on the initial conditions. Hawking's derivation of black hole evaporation seemed to carry as a corollary that even this connection was broken, somewhere between the formation of the black hole and its evaporation, with the Hawking radiation spectrum dependent only on the black hole's macroscopic mass, spin, and charge.

These days people seem to favor the other view, that Hawking radiation does still carry the quantum information of everything that went into the black hole, albeit in a scrambled form. This is certainly the opinion in string theory, for example. In string theory, one should be able to describe the evaporation process in detail. Juan Maldacena's thesis (just before he discovered AdS/CFT) did this for some kind of supersymmetric black hole, describing the black hole as a bound state of branes, and the thermodynamic properties like its temperature, arising from a gas of open strings attached to the branes. But that was probably a large black hole in AdS space, where the Hawking radiation can't properly escape, and instead you have an equilibrium between particles falling in and particles leaking out. As far as I know, string theory still doesn't have a worked-out model example, of complete evaporation of a black hole.

 

[Suekdccia]

These days people seem to favor the other view, that Hawking radiation does still carry the quantum information of everything that went into the black hole, albeit in a scrambled form

Does that mean that the black hole emits all the particles that went into it but in a disordered way?

 

[Nugatory]

Does that mean that the black hole emits all the particles that went into it but in a disordered way?

No.
It means that the particles will interact the way that quantum mechanics predicts as mass-energy enters the black hole and is eventually emerges as radiation. There's no reason why this interaction should preserve the identities of the incoming particles that make up this mass energy, any more than there is any reason to expect a positron and an electron to come out of a box just because that's what we put into the box.