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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

Dustin Soodak
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    Sounds like you want to use the Zel'dovich radiation, for that you need quantum electrodynamics combined with relativity. If you use the Penrose process you only need relativity to calculate the magnitude, which is easier to calculate, but harder to achieve since the test particle has to split in two close to the black hole. – Yukterez Jun 29 '23 at 10:31
  • Actually, just using frame dragging effects. A Spinning BH can add energy to nearby photons (battery discharge) ( look up "black hole bomb") and incoming light will add to its angular momentum if it orbits a bit first (battery charge). I guess I should have been more specific. – Dustin Soodak Jun 29 '23 at 20:55
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    Does this answer your question? Gravitational lensing redshift around a Kerr black hole - Specifically the answer is no, frame dragging does not change the energy of photons (when the energy before and after is properly measured in the same coordinate system). – safesphere Jun 30 '23 at 06:01
  • The intent of my question was to explore the phenomenon that is used to make a "black hole bomb". The technical term (which appears as a response to one of the comments on the page you linked to) seems to be "superradiant instability" which evidently involves quantum effects (not just frame dragging). Instead of amplifying existing photons it adds additional ones. I still think my thought experiment is valid, but I'll have to study this topic in more detail in order to frame it correctly. – Dustin Soodak Jun 30 '23 at 19:45

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