## Extracting energy from a black hole via gravitational blueshift

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Volbla
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### Extracting energy from a black hole via gravitational blueshift

Spoiler:
cheat.png (7.85 KiB) Viewed 2796 times
We have a satellite at a highly eccentric orbit (A) around a black hole. We also have a satellite or a number of satellites at a low-eccentricity orbit (B) higher than A. At A's periapsis it is sent a laser beam which gets highly blueshifted from the black hole and therefore more energetic, and the satellite absorbs it and stores the energy in a battery or some such. At apoapsis A will beam the energy back to B, which is now higher than when B sent it.

1: Does this work or is the energy somehow lost again on A's climb or in some other way? 2: If it does work, where is the added energy coming from? Does it come from the black hole or from space or is it even a violation of the conservation of energy?

Heimhenge
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### Re: Extracting energy from a black hole via gravitational blueshift

This obviously doesn't work for kinetic energy extracted from falling mass, since you'd lose that climbing back outa the gravity well. With photons it get a bit trickier but I'm pretty sure conservation of energy would still hold. Nature can be clever when you try to get something for nothing. I'm no specialist in general relativity, but my intuition tells me time dilation would somehow offset the gain in photon frequency.

ijuin
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### Re: Extracting energy from a black hole via gravitational blueshift

It’s not the time dilation where you lose the energy again—it’s plain old e = m * c^2. Your satellite climbing out of the gravity well is heavier by an amount equal to the energy gained by the photon.

Heimhenge
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### Re: Extracting energy from a black hole via gravitational blueshift

Yeah, that makes sense and it's pretty simple. Like I said ... Nature had to intervene somewhere to thwart the free energy. But there's so many symmetries in GR that I'd bet it could explained by time dilation too. Kinda like how you see length contraction in one frame of reference, and time dilation in the other (to explain how a length contracted ship gets through a timed trapdoor).

doogly
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### Re: Extracting energy from a black hole via gravitational blueshift

You can extract energy out of a rotating black hole by slowing down the rotation though. This is fun.
https://en.wikipedia.org/wiki/Penrose_process
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Volbla
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### Re: Extracting energy from a black hole via gravitational blueshift

ijuin wrote:It’s not the time dilation where you lose the energy again—it’s plain old e = m * c^2. Your satellite climbing out of the gravity well is heavier by an amount equal to the energy gained by the photon.
What does that impact though? The mass of a satellite has no bearing on its orbit, right? (As long as it's much smaller than the orbited body.) Maybe the momentum of the light beam would give the satellite a push in a bad direction, but that seems like it could be overcome by controlling where from you send the beam.

Heimhenge wrote:Nature can be clever when you try to get something for nothing.
I know, right? But i want to find the coding trail for how that happens

Heimhenge wrote:This obviously doesn't work for kinetic energy extracted from falling mass, since you'd lose that climbing back outa the gravity well.
At first i thought "Yeah, that's because the mass of an orbiting object will remain constant whereas a beam of light will energize." but is that untrue? Is there a relativistic mass in strong gravity that will impact what mass the A satellite gains from the beam, and then maybe changes proportionally when it climbs out?

Tub
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### Re: Extracting energy from a black hole via gravitational blueshift

Volbla wrote:The mass of a satellite has no bearing on its orbit, right?

That's true for a constant mass, but you're adding and removing mass mid-flight.

It's true for a Ferris wheel that (ignoring friction) it will keep its rotational speed forever, regardless of mass. But if you start loading cinder blocks at the bottom and unloading them at the top, the wheel will slow down. You did not create a free elevator.

What ijuin wrote is correct, but if you don't like the Ferris wheel analogy, then you can also argue about it using momentum.

Volbla wrote:Maybe the momentum of the light beam would give the satellite a push in a bad direction, but that seems like it could be overcome by controlling where from you send the beam.

You've designed the light beam to be accelerated directly towards the black hole. That counts as a "bad direction" for all orbits under any circumstance. You would need additional energy to maintain orbit.

PM 2Ring
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### Re: Extracting energy from a black hole via gravitational blueshift

Gravity is a conservative force, so the net work over a closed loop must be zero.

Conservation of momentum is certainly important, but I don't think that's the solution to this puzzle, since we can make the masses of the satellites huge, so they have large momenta relative to that of the beams of light energy being transmitted. But I guess eventually the momentum exchanges will modify both orbits.

IMHO, the key is that blue shifting and red shifting are intimately related to time dilation. Blue shifting and red shifting don't create or destroy energy, they simply compress it into a shorter time interval and stretch it out over a longer time interval. If we replace A & its equipment by a fibre optic cable, it should be obvious that the frequency that comes out at the far side of the B orbit is identical to the frequency that went in on the near side of the B orbit.

Tub wrote:It's true for a Ferris wheel that (ignoring friction) it will keep its rotational speed forever, regardless of mass. But if you start loading cinder blocks at the bottom and unloading them at the top, the wheel will slow down. You did not create a free elevator.

Very good point, Tub!

Eebster the Great
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### Re: Extracting energy from a black hole via gravitational blueshift

doogly wrote:You can extract energy out of a rotating black hole by slowing down the rotation though. This is fun.
https://en.wikipedia.org/wiki/Penrose_process

This is far too efficient. I prefer to wait until the universe has cooled down to a lower temperature than the black hole and collect its Hawking radiation for the next 1075 years.

ijuin
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### Re: Extracting energy from a black hole via gravitational blueshift

The Penrose process only extracts the rotational energy however. As far as we know, Hawking radiation is the only method for extracting its rest mass.

Volbla
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### Re: Extracting energy from a black hole via gravitational blueshift

Tub wrote:That's true for a constant mass, but you're adding and removing mass mid-flight.

It's true for a Ferris wheel that (ignoring friction) it will keep its rotational speed forever, regardless of mass. But if you start loading cinder blocks at the bottom and unloading them at the top, the wheel will slow down. You did not create a free elevator.
Mm... In which case the issue would be that the satellite only has more mass on half of its orbit (the climb). What keeps creeping into my head, though, is that as soon as a satellite gains mass, the orbited body should start pulling it harder, cause gravity is nice like that, and that will keep the orbit constant. I'm not sure the ferris wheel comparison works because the center of gravity is not in the middle of the wheel, it's entirely outside it. The cinderblocks you load at the bottom are still pulled down rather than "up" as they would in an orbit.

My fear is that this line of thinking is too newtonian which obviously isn't enough to accurately describe this situation, but i don't know enough relativity to do that ¯\(ツ)/¯

PM 2Ring wrote:IMHO, the key is that blue shifting and red shifting are intimately related to time dilation. Blue shifting and red shifting don't create or destroy energy, they simply compress it into a shorter time interval and stretch it out over a longer time interval.
That is interesting! So if we sent a continuous laser beam from B for, say, one second, A would recieve that beam bluer but in a shorter burst and therefore the same total energy? Is that right? How would that work for a single photon?

Something else i just thought of. At its periapsis the satellite will be traveling at its fastest. If it's accelerated to relativistic speeds, could that somehow cancel the gravitational effects? Would the light not appear blueshifted at all? Relativity is complicated~

I think what prompted this question in my head was that way back at uni someone asked after class what happens to the energy of cosmologically redshifted light, and the professor's response was that "Conservation of energy doesn't seem to hold on a cosmological scale." Maybe that was just an off-the-top-of-his-head response, but the way he said it made it sound like this was commonly acknowledged.

Though... even if that part is true, maybe there's a significant difference between cosmological and gravitational redshift.

Eebster the Great
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### Re: Extracting energy from a black hole via gravitational blueshift

I'm not sure I understand the Ferris wheel analogy. Whether or not a satellite's mass is constant, if the only force acting on it is gravitational, its acceleration should not depend on its mass. That's not the problem with OP's proposal. You definitely have to consider relativistic effects, since the only way he is gaining energy in the first place is through gravitational blueshift.

The plan definitely won't work, because it allows the system to return to its initial state except with a charged battery. But it's not super obvious why it won't work.

gmalivuk
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### Re: Extracting energy from a black hole via gravitational blueshift

Volbla wrote:
ijuin wrote:It’s not the time dilation where you lose the energy again—it’s plain old e = m * c^2. Your satellite climbing out of the gravity well is heavier by an amount equal to the energy gained by the photon.
What does that impact though? The mass of a satellite has no bearing on its orbit, right? (As long as it's much smaller than the orbited body.)

It's still much smaller, but not quite as much smaller.

You can ignore the mass of the much smaller object and get a very good approximation of the orbit, but that approximation gets worse as the mass disparity decreases. Think of it this way: obviously a small satellite orbiting a black hole is going to look very different than a second (equally massive) black hole, right? Well, there's no point where the system discontinuously shifts from being "a small thing orbiting a big thing" to "two big things in a binary orbit". There's a smooth transition from one to the other. And that means adding mass to the smaller object, even if it's just the mass-equivalent of a single blue-shifted photon, ever so slightly changes the dynamics of the orbit.
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Tub
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### Re: Extracting energy from a black hole via gravitational blueshift

The Ferris wheel was in response to ijun's "climbing out of the gravity well" wording. It's not a perfect analogy, but it shows that if you take a system that's stable due to inertia and use it to lift stuff against gravitation (i.e. do work), you will affect the system. If the analogy doesn't work for you, PM 2Ring posted a link to a boring rigorous explanation.

The crux is that the diagram shows the photon to gain energy on the way in, and then be transported back out for free. The "for free" does not happen.

If the satellite just "picks up" a payload and "drops it off" at a higher point, then it has done work, and that can't happen for free.
Equivalently, if you like to talk orbits, then the payload must be accelerated to orbital velocity before you can claim free orbital transportation, and that acceleration isn't free.
Equivalently, my previous argument about momentum holds; momentum and energy of a photon are proportional, so your orbit loses momentum at the same rate you gain energy.

All of these descriptions (plus a dozen more, plus the whole conservation of energy thing) tell us that either the photon will arrive back at B with no more than the energy it left with, or the system has been changed during the transfer, and you need to spend the energy to undo the damage. If none of those explanations satisfy, then I'm not sure what will.

Eebster the Great wrote:You definitely have to consider relativistic effects, since the only way he is gaining energy in the first place is through gravitational blueshift.

You can draw the same diagram with a sufficient distance from any source of gravity, replacing the photon with an accelerated free-falling pebble. That should minimize relativistic effects. It should also minimize the amount of explanations that discount momentum.

Going relativistic is only going to make the formulas more complicated, but I don't see where it would fundamentally change the problem.

gmalivuk
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### Re: Extracting energy from a black hole via gravitational blueshift

Also, if you consider the orbit in a rotating one-dimensional frame, then gravity again is always pointing "down" and inertia (which becomes centrifugal force in this case) works against it to pull back up. It ends up looking very similar to considering height only for the Ferris wheel.
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ijuin
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### Re: Extracting energy from a black hole via gravitational blueshift

A one-dimensional frame does not contain angles, therefore it can have neither angular momentum nor rotation.

gmalivuk
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### Re: Extracting energy from a black hole via gravitational blueshift

That's why you have to account for those things with the effective potential.
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Volbla
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### Re: Extracting energy from a black hole via gravitational blueshift

Ok, i've realized why the increase in mass is important here. The added mass does not have any momentum in the current direction of the satellite, and since momentum is conserved the satellite will slow down, lowering its apoapsis and, if you repeat the process, changes its orbit closer and closer to a circular one. So any energy "extracted" will be taken from the inner satellite's orbit(?).

This did lead me to two different questions though. The first is a change of setup. Send your light beams this way instead:
Spoiler:
cheat2.png (7.03 KiB) Viewed 2339 times
In this case the momentum of the light will add/subtract to complement A's orbit. Simplest calculations would put the momentum of the satellite at p=mv, or v=p/m. The momentum added by the light will be pl=E/c, and the mass it adds is ml=E/c2. So the change in the satellite velocity is Δv = (p+E/c)/(m+E/c2) - p/m. Right? Now, it seems to me like this is positive because the numerator of the first term increases more than the denominator since E/c is greater than E/c2. Or in other words, the light adds more momentum than it adds mass. In that case, what if we beam some light from this direction and some light from the opposite direction to keep the satellite velocity constant. Won't its orbit then stay the same and the original problem persists?

However! You don't add momenta linearly in relativity, do you... How do you add them? I don't know, but if Δv ends up less than 0 there should be no way to maintain the satellite orbit.

The second question i thought of is more general. With this new setup the light won't fall straight, will it? It will be curved by the gravity well. At that point it starts to look like simply dropping an object, so my questionn is this: Is gravitational blueshift analogous to the kinetic energy gained by a falling mass? My rationale for why very strong gravity is needed for noticable frequency shift would be that light is already all momentum, so you need a lot of change in potential energy to significantly change its momentum. Matter, on the other hand, can easily have zero momentum, so any energy added will quickly make a significant difference.

Is that at all close to true or is there more to it than that?

gmalivuk
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### Re: Extracting energy from a black hole via gravitational blueshift

Volbla wrote:
Ok, i've realized why the increase in mass is important here. The added mass does not have any momentum in the current direction of the satellite
While that's also an important factor, I already explained that simply increasing the mass would itself have an effect on the dynamics of the system, though not, I think, in a way that by itself proves you can't get energy out of your scheme.

(If you speed up a mass in the direction of the satellite before attaching it to the satellite, then you yourself have put work into the system, which of course you can then extract from the system later when you remove the same mass.)
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### Re: Extracting energy from a black hole via gravitational blueshift

Assuming the satellites are moving counterclockwise based on the direction of the photons, you'd be increasing the AP and lowering the PE until the inner satellite enters the event horizon and is lost.

Volbla
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### Re: Extracting energy from a black hole via gravitational blueshift

gmalivuk wrote:While that's also an important factor, I already explained that simply increasing the mass would itself have an effect on the dynamics of the system
By changing the pull on the black hole by the satellite? Yeah, that too.

gmalivuk wrote:though not, I think, in a way that by itself proves you can't get energy out of your scheme.

(If you speed up a mass in the direction of the satellite before attaching it to the satellite, then you yourself have put work into the system, which of course you can then extract from the system later when you remove the same mass.)
Myes. I think i low-key want a giant diagram for the entire energy flow of the system, though i've accepted half-understandingly that this scheme won't generate free energy.

But beyond that i reckon i just want to understand what gravitational frequency shift actually entails. What does it imply about the energy of the light and the body that causes it? I should study more (:

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