What is the maximum charge/discharge efficiency of a spinning black hole when used as a battery via frame dragging effects?
Charging: I'm pretty sure the best way to add to its angular momentum (in terms of angular momentum added per mass/energy dropped in) would be to aim a reasonably parallel beam of light (such as a laser or collimated waste heat) so that it momentarily orbits just below the photon sphere in the direction of spin before dropping in. The total momentum (black hole plus light) won't change from the time it is orbiting to when it falls in, so you could just use a formula for angular momentum of an orbiting photon.
Discharging (lots of literature on this but mostly too technical for me): You can extract energy later by sending an infrared laser beam in so it orbits just above the photon sphere before exiting. Repeat the process with distant mirrors (outside of most of the frame dragging effect) till each photon has many times the energy it started with. Using a BH with a larger angular momentum will mean fewer orbits necessary, though I don't know how this affects the energy conversion ratio.
Is the angular momentum added per energy in photons absorbed the same as the angular momentum decrease per photon energy extracted? It would probably be possible to figure out the rest by simulating photon orbits in a Kerr metric.
Presumably, the total efficiency is significantly less than 100% unless the extra entropy is somehow dumped into the quantum complexity of the BH.
Dustin Soodak
