A Dyson sphere around a black hole

For a realistic visualization of what one would see when falling in a black hole see https://jila.colorado.edu/~ajsh/insidebh/schw.html

EDIT: Inb4 the downvotes.

A.) Keep it in place and not hit the star/black hole.

B.) Avoid it being demolished by intercepting every piece of space trash, comet, asteroid in a solar system?

I don't see any requirement why an intelligent civilisation would need to grow its population forever. It seems far more intelligent to attack the cause of the energy need instead of building crazy structures like Dyson spheres around black holes.

Umm...

The sun is about 2×10^30 kilograms. The rest of the solar system is about 3×10^27 kilograms and we kind of need it to live on and make things with. Put in other words, the entire solar system including the Sun is 1.0014 Solar masses. Why not go with the process we have rather than fusing everything we have to do the same thing?

If you're saying that we don't need that much energy then I think that's pretty meaningless since we have no idea what we could get up to or need in the far future.

The technology required to build a tier 1 swarm is not advanced. All you need is the ability to build a thin reflector (aluminium foil would work) with radio and a basic onboard computer. You do not even need onboard propellant because a reflector can generate the required thrust for minor corrections with solar pressure alone. These reflectors can then concentrate that light from close in to the star out to collectors further out in the system. This essentially makes your habitable zone as large as you want since you can also light entire planets this way and only utilize less than a percent of a percent of your total energy budget.

The real challenge is having good enough automation to construct and send these stations out without requiring too much oversight, and getting good enough at construction off earth (since you really don't want to deal with that gravity well). We're definitely close to having the required automation technology and we should be performing the first manufacturing off earth before the end of the next decade.

Artificial fusion can be made far more efficient than the fusion in the core of our sun, yes. However, the sun outputs enough energy to light 2 billion earths worth of surface. Moreover, it essentially contains all of both the hydrogen and rocky material in the solar system with the other bodies being essentially a rounding error in comparison, so even in a controlled fusion based economy, you would still create a Dyson sphere like construct since you would be using that star as your main fuel and mass source.

Black holes though? They make even aneutronic fusion look like a fire cracker in comparison. You're getting less than a percent mass energy conversion with even the best theoretical fusion models there are, whereas with black holes, you can get anywhere from 16% to 40% depending on the technique and mass range of the black hole. Stellar black holes have so much energy inside that they would dwarf even our star (consider that their progenitors were stars with far more mass than our own and with an even bigger disparity in power output). They also last for periods of time that make even red dwarfs look like still births. If you could make artificial ones in the gigaton and megaton ranges, then they can also make for amazing batteries. In this case, you are able to tap the hawking radiation emitted for power and this promises potentially even greater efficiencies than the stellar mass ones (albeit, you would not be gaining a net power gain here, this is strictly for power storage and potentially gravity generation purposes).

P ~ A · T⁴ ~ 1/M²

So while a larger total amount of energy can be extracted from a supermassive black hole (because it's more massive – duh), it also takes much (much!) longer to extract a given amount of energy: A supermassive black hole's mass is in the order of 10⁶ to 10⁹ solar masses, i.e. 10⁶ to 10⁹ times the mass of a stellar-mass black hole, meaning that its power is just 10^-12 to 10^-18 × the power of a stellar mass black hole.

https://arxiv.org/abs/2106.15181 is the preprint.

The authors' model rests on an asymptotically flat incoming Vaidya spacetime[1] equipped with a cosmic microwave background that dilutes away over time (like the real CMB) but without the worries of tracking the cosmological constant sufficiently near the black hole.

They unsurprisingly find that the energy budget from the background light that collides into the black hole in this model is an uninteresting part of the system's extractable energy budget. The real CMB has a low energy-density at all times when our universe has star-filled galaxies in it, and one would need a high boost to get significant power from it, or equivalently, one would have to gravitationally modify the energy-density locally. (That boost could be found by an observer hovering just outside their model non-rotating black hole, or in a different model where (for example) where a black hole's rotation can lead to an observer developing angular speeds approaching the speed of light; however there is no obvious way to transmit harvested power of this sort "up" to a Dyson sphere thanks to gravitational redshifting at least. The authors admit that calculating an energy budget which relies upon black hole rotation is too hard, and move on).

Skipping over the accretion disk section, which I'll return to, the authors also find that in the absence of angular momentum and, an incoming spherically symmetrical uncharged "rain" onto the black hole does generate significant outgoing radiation, which is also unsurprising. This is after all essentially what the CMB is, just with a higher "molecular weight" than light. Of course this particular rain is unphysical: our universe is populated by clouds of gas, and stars, which periodically -- not uniformly in time -- intersect black holes like the one in our galactic centre [2], causing occasional flares. They do not spend much time describing an integral approach around this. For what it's worth most principled uses of the Vaiyda metric consider outgoing radiation as an easy proxy for Hawking radiation (or even more often for modelling the cooling of white dwarfs). A massive incoming Vaiyda "anti-shine" has some interesting consequences or requirements for regions far from a black hole with lifetimes of more than a few million years!

The authors do not properly explain how they equip their model with a relativistic jet (they repeat an empirical luminosity relationship between astronomically observed jets accretion disks, but no causality is found in their model, and their model is different from "real" astrophysics) which is quite striking given their everywhere spherically-symmetric, exactly zero angular momentum, and exactly zero magnetic charge setting for for their CMB and Bondi accretion analyses. Their Chou 2020 reference [3] underpinning their relativistic jets purports to describe a spacetime where the authors break this no-angular-momentum condition. From that breaking they take spherical symmetry into axisymmetry, and with some addition of magnetic interactions, they arrive at an environment that might plausible host relativistic jets. But they also suddenly introduce significant consequences of angular momentum and other nongravitational charges near their model black hole that are not accounted for in their CMB or Hawking analyses. They do not explain how to reconcile their findings from two qualitatively different spacetimes, nor do they attempt an argument that the quantitative differences vanish "below" the altitude of the Dyson sphere. (Do you have to make an axisymmetric Dyson swarm, where the equatorial collectors have a high orbital angular velocity?)

I think that the authors would have written a more interesting (and challenging) paper if they had chosen to explore the components of the energy budget of their Dyson-around-a-black-hole system using a gravitational and matter background that does not change from subsection to subsection.

That they didn't raises two questions I think are large.

Firstly, can they get their §2.6 relativistic jets somehow without introducing both angular momentum and magnetic interactions? (The formation of relativistic jets is a live area of current research).

Alternatively, can they find the heavy calculation lifting in other published work for their energy estimates from CMB-infall and infall-onto-accretion-structure physics? Their Chou 2020 references at least shows that they are competent to do a wide search for papers which purport to do that kind of heavy lifting. Their §2.3 already refers to other work in accretion disc physics that reasonably covers both extremes of angular momentum, but there's a gap between the two which is likely interesting for relativistic jets that an be "mined" by their Dyson sphere, and closer to the spin parameters of known black hole candidates.

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[1] §2.4 could be much clearer about this, especially in light of the "Kerr-Vaiyda" metric they found in [4]; they consider a vanishingly small a parameter (sometimes implicitly) whenever they discuss their model black hole, and resile from the consequences of a significant nonzero spin, except briefly for the case of the maximum possible spin. Perhaps they found it easiest to import the maths from [4]'s results accepting them as good especially in the limit where a vanishes, rather than sticking to a more widely used model -- https://en.wikipedia.org/wiki/Vaidya_metric. After a brief glance at the edit history, I have stray thoughts about the timing of the introduction of [4] at the end of that wikipedia page.

[2] examples https://www.pbs.org/newshour/science/massive-gas-cloud-colli... https://phys.org/news/2021-07-milky-supermassive-black-hole.... and, in a not-too-distant galaxy, https://www.sciencealert.com/arp-299-supermassive-black-hole...

[3] Chou 2020 is https://doi.org/10.1016/j.heliyon.2020.e03336 (pay-for-publication open access by bottom-feeding Elsevier). I believe the author to be https://www.researchgate.net/profile/Yu-Ching-Chou where one finds a link to this reference, and that the publication record of the single-author relativity papers listed there speaks for itself.

For a meteor it makes no difference if gravity is coming from a planet or a black hole of the same mass. The only difference is that once you get very close - the gravity changes much quicker (because black hole is much smaller and denser than a planet) so you will be ripped apart.

I’ve lost my keys, and these guys are asking me to retrace my steps while you’re asking me to consider the machinations of hitherto sleeping whimsical gods. I’ll try your thing next, but first I’ll do the other guys.