Utilising Black Holes as a potential energy source

Question

I'm aware of the Penrose process and the basic physics behind that. Also, I know that the Blandford-Zjanek process (That is potentially responsible for the relativistic jets). Aside from these two, and Hawking Radiation, what other methods or theories are there for extracting energy from a black hole, or the phenomena associated with one? Of course, all these ideas neglect the engineering challenges - assume an infinite budget and an advanced civilization. Thanks!

Answer 1

Great question. Black holes are some of the brightest objects in the universe. While we think they require the Blandford-Znajek (BZ) mechanisms to produce things like Relativistic Jets, the bulk of the light (emission) they produce is just the efficient thermalization of gravitational energy when material falls into (`accretes' onto) them.

The simplest way to think about this, is how much energy must be (generally and approximately) be released for material to accrete onto a black hole. The binding (gravitational potential) energy is:

$$\varepsilon \approx \frac{1}{2}\frac{GMm}{R}$$

The radius down to which matter can accrete is roughly the Schwarzschild Radius,

$$R_s = \frac{2GM}{c^2}$$

So the energy of material at the Schwarzschild radius is roughly,

$$\varepsilon \approx \frac{1}{2} \frac{GM}{R_s} \approx \frac{1}{4} mc^2$$

This means that something like 1/4 of the entire mass-energy of accretion material is available to produce emission. Generally, from more precise modeling, the 'efficiency' (fraction of energy available) is more like $\sim 10\%$. Still, if you compare this to something like nuclear fission which only converts less than $1\%$ of the mass to energy, then black holes are outrageously efficient!

So even without complicated BZ/Penrose like processes, just normal accreting black holes are extremely effective at emitting energy. So we'd just need to put super-efficient solar panels (etc) around a BH and we're set.

Answer 2

Utilising Black Holes as a potential energy source

Have I got a surprise for you!

I'm aware of the Penrose process and the basic physics behind that.

Be wary of Penrose. He has a habit of appealing to Einstein's authority then flatly contradicting the guy. And then he'll tell you about the parallel antiverse and other fairy tales:

Also, I know that the Blandford-Zjanek process (That is potentially responsible for the relativistic jets).

Yeah yeah, it still requires a rotating black hole. Only the "coordinate" speed of light at the event horizon is zero. You'll have read reports like Monster Black Hole Spins at Half the Speed of Light. So what's half of zero?

Aside from these two, and Hawking Radiation, what other methods or theories are there for extracting energy from a black hole, or the phenomena associated with one? Of course, all these ideas neglect the engineering challenges - assume an infinite budget and an advanced civilization. Thanks!

There's total conversion of matter to energy. Let's use a brick. An ordinary house brick. And all you have to do to your brick, is drop it. See the second paragraph here where Einstein said this:

"Second, this consequence shows that the law of the constancy of the speed of light no longer holds, according to the general theory of relativity, in spaces that have gravitational fields. As a simple geometric consideration shows, the curvature of light rays occurs only in spaces where the speed of light is spatially variable".

You drop your brick, and it falls faster and faster and faster because the speed of light is spatially variable. Its falling speed at some location relates to the difference in the speed of light at your position and at its position. But the speed of light at the event horizon is zero, see John Rennie saying the same here. So left unchecked, after the halfway point, the brick would be falling faster than the local speed of light at that location. That's not going to happen because of the wave nature of matter. Something's got to give, and it's your brick. It breaks up into gamma radiation* and what you get is a gamma ray burst. Sounds unusual I know, but this is the original "firewall". See An Apologia for Firewalls by the AMPS crew and there in reference 87, is this:

F. Winterberg, "Gamma Ray Bursters and Lorentzian Relativity", Z. Naturforsch. 56A (2001) 889-892.

Here's the full paper here. The abstract says this:

"In the dynamic interpretation of relatively by Lorentz and Poincaré, Lorentz invariance results from real physical contractions of measuring rods and slower going clocks in absolute motion against an ether. As it was shown by Thirring, this different interpretation of special relativity can be extended to general relativity, replacing the non-Euclidean with a Euclidean geometry, but where rods are contracted and clocks slowed down. In this dynamic interpretation of the special, (and by implication of the general) theory of relativity, there is a balance of forces which might be destroyed near the Planck energy, reached in approaching the event horizon. In gravitational collapse, the event horizon appears first at the center of the collapsing body, thereafter moving radially outward. If the balance of forces holding together elementary particles is destroyed near the event horizon, all matter would be converted into zero rest mass particles which could explain the large energy release of gamma ray bursters."

See this old Wikipedia firewall article where Winterberg is mentioned. There's some kind of priority dispute here, and Winterberg has been complaining about censorship. Hence you haven't heard of this. But anyway, I haven't met anybody yet who can explain why this is wrong. I don't think it is.

^{* and maybe neutrinos.}