|MadSci Network: Physics|
Ouch… you are definitely way out there on the leading edge! The first question is can such a thing as a mini black hole exist?
A micro black hole, also called a quantum mechanical black hole and inevitably a mini black hole is simply a black hole around which quantum mechanical effects play an important role.
The usual way to make a black hole is to allow nature to accumulate enormous amounts of mass until the gravity is so great that even light can not escape. But total mass is not the complete story. What if there was less mass but it was concentrated into a smaller volume? Wouldn’t this create the same effect? The answer is yes…theoretically.
So if we can compress matter to such an extent that gravitational effects, on a very small region of the universe, would be great enough to keep light from escaping, then we would have a small black hole (micro, mini, or whatever)
Hawking and others tell us that such a phenomenon would be very unstable and decay giving off energy in the form of radiation. Any mini black holes created during super nova class explosions in the universe would quickly dissipate. In theory, however, we might create mini black holes in ultra high energy accelerators. So perhaps we can create them, and therefore your question is valid, and they would decay giving off energy…so you want to know how much.
Carl Wolf of looked into the problem. Here are some pertinent extracts from his paper:
The Decay of a Black Hole as a Quantum Process
Department of Physics, North Adams State College, North Adams, MA (01247) USA
By considering the decay of a black hole as a result of the interaction of a quantum system with a dissipative vacuum, or in terms of string theory, the interaction of localized string modes with non-local string modes, we demonstrate how the single parameter representing dissipation can be calculated in terms of known fundamental constants. In view of the uncertainty embodied in all the present theories of black hole decay it is suggested that the approach of this note might provide fresh insight to the problem of black hole decay.
Later the energy of a black hole can be found with:
And in conclusion Carl stated:
It once more lends evidence to the fact that space, time, and matter are inseparable and questions such as CP and T violation might only be understandable when we understand how matter is truly intertwined with geometry through perhaps string theory  or perhaps a theory of gravitation beyond the structure of general relativity.
So it looks as if you have to use a "retarded" Schoedinger equation! That’s how I felt when I had to work with it back in the sixties. But if you look at his energy equation you see a familiar expression:
E = mc2. So maybe Einstein has answered the question for us. Convert 10 micrograms to kilograms:
10 ug = 1E-10 kg. Plug this into Einstein’s general theory of relativity:
E = (1E-10 kg)*(3E8 m/s)^2 = 9E6 Joules
So neglecting complications from time/space distortions it appears as if 10 ug of matter can be converted into about 9 million Joules of energy whether it is done in a nuclear explosion or mini black hole decay.
Seems simple enough but I suspect that there are complications brought on by quantum mechanical effects in such a system.
Keep asking the tough questions,
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