Toffo wrote:Here's a mechanism, or whatever, of getting energy out of a black hole:
http://www.nature.com/nature/journal/v2 ... 030a0.html
The "explosion" would still just be thermal radiation, so this would be covered by my comments about using some kind of heat engine to exploit temperature differences between the black hole's Hawking radiation and some external system at a different temperature.
Toffo wrote:Oh yes, maybe I should tell what my simulation simulates. We take one of those Hawking radiation reflecting containers, put one small and one large black hole in there and wait ... after some time small black hole has evaporated and big black hole has absorbed the evaporated radiation. As there is a radiation wind there, we can put a radiation wind turbine there and get some electric energy out of that contraption.
Do you mean something like a Crookes radiometer? As explained on the wikipedia page this is really another type of heat engine, and this paper explains further:
Put a radiometer into a cold anddark place, for example, a refrigerator. The black surfaces, being good absorbers of light and heat radiation, are therefore also good radiators (by Kirchhoff’s law). They cool down more rapidly than the white surfaces, and the vanes will spin in the reverse to the usual sense. This spinning will come to a halt as both surfaces of the vane approach a new thermal equilibrium. So, too, a radiometer run by a heater will gradually cease its rotation as the vanes attain the same overall temperature. The radiometer run by sunlight, which is converted to heat by the blacksurface, does not stop since it never comes to equilibriumwith the temperature of the incident radiation, that is, the temperature of the sun’s surface.
If instead of a Crookes radiometer, which depends on interactions with the gas in the chamber, you wanted to use a turbine powered purely by radiation pressure, I am not sure if this would work with purely thermal radiation--certainly it shouldn't work in a reflective box filled with only radiation and a turbine if the whole system were at equilibrium, since you can't get any work from a system at equilibrium. In the case of the black holes, even though they are both emitting thermal radiation they are at different temperatures so there should be a gradient in the temperature of the radiation, if the turbine wasn't at a different temperature than the ambient radiation maybe you could only get the turbine to spin using radiation pressure if it was large enough so there was a significant temperature difference in the radiation hitting different parts of it. Or it may be that even in a small region where there's very little temperature difference between sides, if there is a significant temperature difference on larger length scales, you could measure significant energy flow (as measured by the Poynting vector) in the smaller region, presumably traveling away from the direction of the faraway hot region and towards the direction of the faraway cold region--I'm not really sure if this is the case, I haven't studied the thermodynamics of radiation much.
Anyway, no matter what system you use, the work you can do with the turbine is presumably going to be much smaller than the total energy that gets emitted by the smaller black hole before it evaporates completely. You said "the released energy is only about 1/4 of the total energy of the two black holes", but even if that calculation is correct (I don't know the details of how you arrived at it so I can't judge), most of that energy is not going to be converted into work by the turbine(s), agreed? So how does this relate to your argument about how "you can not fuse entropic stuff and extract lot of energy"? When you said "extract a lot of energy" you were talking about doing work, right? Also note that the entropy does increase when the mass/energy of a smaller black hole is absorbed into a larger one, since the entropy of a black hole is proportional to the square of its mass, so for example if you have two black holes of masses 3/4*M and 1/4*M and they merge into a black hole of mass M, the initial entropy is equal to some constant time (9/16 + 1/16)*M^2 = 10/16 * M^2 and the final entropy is equal to the same constant times M^2. And generally when you have a closed system that starts at a lower entropy and evolves to a higher one, you can do some work along the way.