# Hawking radiation of a charged black hole

• B
SlowThinker
I was thinking about the title but after searching Arxiv, PF and the internet in general, my confusion has only increased. I have a few questions:
1. Often I see units where ##G=c=\hbar=1##, but what is the charge of an electron in these units? Everyone says M=Q as if it was somehow obvious how much charge corresponds to 1 kg.
2. Does a charged black hole, far away from other matter, keep its charge, or does it get rid of the charge by emitting more electrons than positrons (or the reverse)?
I don't quite understand https://arxiv.org/abs/1503.04944v2 but it seems to say that the charge is constant:
bottom of page 7 said:
Namely, the field equations require that Φ is a real field and the electric charge Q is constant.
but the last page of https://arxiv.org/abs/hep-th/0602146 clearly has equations for outgoing current flow. Again, the actual math is well outside my knowledge.
3. If I throw matter into a black hole, and gather the outgoing radiation, and convert it into matter, have I just violated the conservation of lepton number and baryon number?

While I am at it,
4. If I surround a black hole with a charged (metal) sphere, will its Hawking radiation be the same as without the sphere, namely, will it emit charged particles? (If needed for the answer, the excess opposite charge is stored in a space station orbiting the sphere.)

• Dale

Mentor
what is the charge of an electron in these units?

See the table here:

https://en.wikipedia.org/wiki/Geometrized_unit_system#Geometrical_quantities

It gives the conversion factor from conventional charge units (SI) to geometric charge units (length).

Does a charged black hole, far away from other matter, keep its charge, or does it get rid of the charge by emitting more electrons than positrons (or the reverse)?

It depends on what model you're using. If you're using classical GR + classical Maxwell's Equations, the charge of the hole is a constant. If you want to try to model the possibility of the hole emitting charged particles, you would have to use quantum gravity; the papers you link to appear to be trying to construct such models. This is an open area of research so I don't think we have any firm answers at this point as to what actually happens.

If I throw matter into a black hole, and gather the outgoing radiation, and convert it into matter, have I just violated the conservation of lepton number and baryon number?

I assume you're referring to Hawking radiation? Yes, as far as we know the process of forming a black hole and then letting it evaporate by Hawking radiation violates baryon and lepton number conservation. But we don't really know the correct theory for this process, so we can't be sure.

• SlowThinker
Mentor