In the context of energy extraction of spinning black holes, there are two known mechanisms: the Penrose process and the Blandford-Znajek process. The former relies on fragmentation of accreting flow, the latter relies on an external magnetic field

But both of these mechanisms are usually studied for supermassive galactic black holes.


How efficient and/or feasible would be these energy extraction processes when applied to micro blackholes? ($M < 10^{15}$ kg)

Useful summary of both processes in the context of relativistic jets. Penrose method seems to be disfavoured in recent years due to the unphysicality of the required relativistic fragmentation step in the ergosphere.


1 Answer 1


How efficient would be these energy extraction processes when applied to micro black holes?

I fear the efficiency would be zero percent. See the Blandford–Znajek process on Wikipedia where you can read that the power can be estimated as the energy density at the speed of light cylinder times area:

$$P=B^2\left(\frac{r}{r_c}\right)^4 r_c c=\frac{B^2 r^4 \omega^2}{c}$$

The speed-of-light cylinder is where the plasma can't rotate with the black hole, because if it did it would be going faster than light. Only take a look at the propagation of light in non-inertial reference frames on Wikipedia. See this: at the event horizon of a black hole the coordinate speed of light is zero. So the black hole has its own speed-of-light cylinder at the event horizon, and since c = 0 at that location:

$$P=B^2\left(\frac{r}{r_c}\right)^4 r_c c= 0$$

You might challenge that and say the local instantaneous proper speed of light is always c, but a stopped observer doesn't make a stopped clock tick$^*$. Or you might refer to the Penrose process, wherein the rotational energy of the black hole is located, not inside the event horizon of the black hole, but on the outside of it. But take a look at this: In the process, a lump of matter enters into the ergosphere of the black hole, and once it enters the ergosphere, it is split into two. The momentum of the two pieces of matter can be arranged so that one piece escapes to infinity, whilst the other falls past the outer event horizon into the hole. The escaping piece of matter can possibly have greater mass-energy than the original infalling piece of matter, whereas the infalling piece has negative mass-energy. I'm sorry, but I don't buy that. I know of no matter which is comprised of negative energy. (Apart from the space amoeba of course, LOL!) And no fields either. Gravitational field energy is positive, not negative, hence the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy. Yes, binding energy is said to be negative energy, but in truth it merely indicates that there's a mass deficit, and less positive energy present. Not a negative mass. IMHO you'd be better off with Winterberg's firewall, which rips matter into energy with 100% efficiency. There's a mention of it on an old version of the Wikipedia Firewall article. I worked out there was a GRB issue here a few years back, and was surprised to find Winterberg had come up with it in 2001. I think it's right. But hey, maybe I should ask a question about it.

$^*$ It's an optical clock.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.