Sunday, 2 August 2015

Utilising Black Holes as a potential energy source


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



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.


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