Could black holes be a better source of energy than stars?

In my story, set in the far(ish) future, humanity discovers a way to extract energy from black holes (perhaps via the Penrose process?), which sparks conflict as various factions attempt to take control over previously useless and dangerous but now suddenly valuable black holes. This energy is extremely valuable because warp drives for faster-than-light travel require massive amounts of power, which made them impractical before the proliferation of Penrose process power plants.

In order for this to make sense, black holes would have to be a better source of energy than whatever humanity was using before, which I assume would be Dyson spheres/rings/swarms/etc. gathering energy radiated from stars.

To see if this is plausible, I attempted to compare the energy output of a Penrose power plant vs a Dyson sphere around the sun.

According to the Wikipedia article about the Penrose process, up to 29% of a black hole's mass energy can be contained in its angular momentum. So, assuming a black hole with the mass of the sun (which I know is too small to become a black hole, but I wanted to compare apples to apples), the total amount of energy that can be harvested from it is $(0.29\cdot1.989\times10^{30})c^2 = 5.18\times10^{46}$ joules.

For comparison, the sun emits a total of $3.9\times10^{26}$ watts.² Over the 5 billion remaining years of the sun's life, assuming its energy output remains constant, it will emit a total of $(5,000,000,000\cdot60\cdot60\cdot24\cdot365)(3.9\times10^{26}) = 6.15\times10^{43}$ joules.

So the black hole has over 800 times as much energy to harvest! But the real question is, how quickly can that energy be harvested?

According to Wikipedia, an object's energy can be increased by up to 20.7% using the Penrose process. That means the equation for how much energy we can get from a given mass is $0.207mc^2$. So, the amount of mass we need to toss into the black hole per second to match the sun is $\frac{3.9\times10^{26}}{0.207c^2} = 2.1\times10^{10}$ kilograms per second. But only half of that mass actually falls into the black hole, the rest can be re-used. So only $1.05\times10^{10}$ kilograms are consumed each second.

How much mass is that? That's about 1.75 Great Pyramids of Giza every second. At that rate, the mass of the moon would be used in $\frac{7.3\times10^{22}}{1.05\times10^{10}} = 6.95\times10^{12}$ seconds, or about 220,000 years.

For the sun, it would be $\frac{1.989\times10^{30}}{1.05\times10^{10}} = 1.89\times10^{20}$ seconds, or a little under 6 trillion years.

Based on the math, it seems plausible. (Assuming you can toss stuff in fast enough.)

So my questions are:

• If a civilization is not advanced enough to harvest energy from black holes, are stars the best source of energy?
• If a civilization is advanced enough to harvest energy from black holes, are black holes the best source of energy?
• Is the Penrose process the best way to harvest energy from a black hole?

By "best" I mean produces usable energy the quickest. I know matter-antimatter annihilation would release energy extremely quickly, but you have to create the antimatter first, which uses a bunch of energy. (In my universe, humanity never figures out how to create antimatter efficiently enough to get a net gain of energy by annihilating it.)

posted about 6 years ago

the_nacho‭

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