A 'Kugelblitz' is defined as a black hole formed purely from light, which is an excitation of the electromagnetic field. Is there a generalization for any energy field? If so, what properties would this have and what would go into creating it?
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1) what properties would such a BH have? Same a BHs formed by the same amount of mass-energy, charge and angular momentum of the mass-energy that goes into the event horizon. That is, a BH has no other properties than those 3, and it does not matter what specific type of matter or energy, or combination of those (with E= $mc^2$ for the equivalence), is the original matter or energy that formed it.
Of course, while evolving or falling into the event horizon different types of mas-energy may have different dynamics and most likely other kinds of energy emitted during the collapse, but once inside the Horizon only those 3 properties determine the BH. That's because of the famous theorem that 'BHs have no hair', all the other properties get radiated away before the BH is formed. In the dynamics you also have to account for the time it takes for all that's going to fall in to get inside the horizon. (And btw in a reference frame at infinity it may take forever).
The forms of the BH solution are all variations of the Schwarzschild solution to include charge and angular momentum. So at the end the BH only has mass, charge and angular momentum.
See the No Hair theorem at https://en.m.wikipedia.org/wiki/No-hair_theorem
2) it's been known for a while that pure gravitational or electromagnetic energy (waves) can form into a BH if concentrated enough. That's answered In a related question at Can a black hole be formed by radiation?
