Blueshifted light has more energy (and momentum) than it did before the blueshift. If it returns to your spacecraft blueshifted, you can get more energy and momentum out of it than you used in sending it. The change in momentum can be used for propulsion.

But what is the nuts and bolts of how it is done? What do you capture the light with? How are you propelled? Are we talking solar panels or sails or some other technology?

Maybe depends on what you want. Do you want momentum transfer (thrust)? A sail, because you get more by reflecting than by absorbing. Or do you want energy (more than just kinetic)? A solar panel, because you only gain kinetic energy from a sail. If you want both energy and momentum, tune the solar panel/sail ratio to get what you want.

Lightsail. You carry a laser and a lightsail. You shoot the laser at the black hole and the laser light gravitationally slingshots around the black hole, returning to you with more energy than you gave the laser. The returning laser light pushes your lightsail. The black hole needs to be moving for this to work, although it doesn't really matter what direction the black hole is moving.

It does very much matter which direction the black hole is moving; it needs to be moving toward you or you won't get any blueshifting effect, which is the entire reason the energy budget works out.

The idea in the paper is to put up a big solar panel. Simply by absorbing the light, you are propelled. And you use the energy in the light, which is more than the energy you used to send it, to send more light.

I think you might gain momentum simply from absorbing the light.

You gain even more momentum from reflecting the light back into the black hole! When you absorb a photon, you gain its momentum. However, when you reflect a photon, you gain twice its momentum to account for the momentum possessed by the photon now flying away from you.

Isn't that a three-fer?

You first emit the photon towards the black hole, momentum gain. Absorbing the photon on the return would be a two-fer, and reflecting a three-fer.

Absorbing the photon would be a two-fer. Reflecting it is just starting the next two-fer. It's two-fers all the way down.

Ooh. Even better, it's like compound interest.

You emit photon 1. It has momentum m. It comes back blueshifted, so you get momentum km, with k > 1. You reflect that back, and you get momentum k^2m...

It's not that simple, because as you start to move away, you redshift the photons you reflect. And the alignment issues are going to be pretty severe. And if you get too much compound interest, the photons may be blue-shifted enough to kill you or damage your ship. Still, the idea is pretty slick.

Also in all slingshot maneuvers you get more the closer you are, so you wanna pour in the most energy the closest you can get.

I can see how you gain energy but you’re also putting yourself deeper into a gravitational well that you’d have to expend energy to get out of.

Wouldn’t it be a wash?

We do this fairly regularly with space probes already.

https://en.wikipedia.org/wiki/Gravity_assist

You steal energy from the object you're slingshotting off. The black holes are slowing (infinitesimally) down every time you do it, gifting their energy to the accelerated object.

Hence the article talking about potentially detecting this sort of behavior by monitoring for prematurely merging and overly eccentric binary black holes.

The paper says that the maximum velocity obtainable would be 2x the rotational speed of the body used. Some such bodies rotate at appreciable portions of the speed of light.

Obviously you cannot exceed the speed of light but it doesn't seem like it would be a wash.

At some level, that's also what glider pilots do to take off from mountains.

Emit low energy photons, expend energy X, receive higher energy photos with energy Y (Y> X)

Maybe this way?

Yes I want my free energy device too.

This isn't a free energy device because you're extracting energy from the rotation of a black hole (this process only works on rotating black holes). After a long enough time, you could extract all of the angular momentum from the black hole using this method.