A few years ago, Vladimir proposed a way of traveling intergalactically quickly using the (then) new abilitiy spaceships had to travel: the warp drive (based on the Alcubierre warp drive). The way it works in SE is it boosts the "absolute speed" of a ship (galaxies/solar systems are fixed in the universe) with a logarithmic factor depending on how high the warp engines are engaged at. In short, the higher your absolute speed, the higher your warp speed will be (although this is a linear increase).
The basic concept was to use black holes to achieve really high speeds by orbiting a black hole elliptically, which would result in speed at the perigee close to the speed of light. Then, engaging the warp drive would allow the ship to escape the black hole at speeds so high intergalactic trips would become just a matter of hours.
As Vladimir proposed this idea, he also talked about decelerating; needing another black hole and another elliptical orbit. In the same way, at the perigee of this orbit, the speed would be close to the speed of light, but as the orbit progressed, the ship would slow down until it hit the apogee where it would be its slowest. The goal would be to have this apogee speed the slowest possible.
Now, all of this sounds cool but right now we can achieve such high speeds using ships without even needing to use a black hole! Intergalactic trips aren't difficult as we can just accelerate our ships to whatever speed we need and go from galaxy A to galaxy B in a short amount of game time. We can also accelerate time, so months or years of travel aren't really an issue.
But what if ships had limited fuel? And what if ships couldn't be self-sustained for an infinite amount of time?
This mechanic then becomes the next best idea to shorten trips and save fuel!
All of this sounds great, but how do we do it more specifically? What kind of black holes should we choose for this kind of maneuver? How do we aim at the other black hole?
The type of black hole
Finding the right black holes for this maneuver is a balance between multiple things: tidal forces, orbital period, orbital speed (for the sake of practicality, I'm ignoring ray emission).
As you may know, the tidal forces of a black hole play a part in why they are lethal up close. You may have heard of spaghettification, which is a highly scientific term meant to describe how objects behave when affected by huge amount of tidal forces. Let's say a courageous astronaut wonders close to a 15 km wide black hole, as he approaches it, his feet will be closer to the black hole than his head. His feet will be pulled more strongly towards the black hole than his head will be, and as this phenomenon gets more and more extreme, he will end up being stretched vertically. Plot twist: the astronaut was actually a plush astronaut! No one has been harmed.
The tidal forces in the vicinity of a black hole's event horizon get lower as the black hole gets more massive. Great! This means by using a supermassive black hole and excluding stellar black holes the ship won't be destroyed by tidal forces!
Now arises a new problem; an orbit around a supermassive black hole can take a really long time. If we were to orbit a supermassive black hole with an apogee at a speed of around 50 km/s and a perigee the closest to the even horizon possible, the orbit could take years! Supermassive black holes can't be viable either.
Intermediate black holes between 5000-15000 solar masses strike the best balance between low tidal forces and quick orbital period. An orbit with an apogee speed of 50 km/s and a perigee approaching the event horizon of one of these black holes can take around a day, but we can "cheat" a little bit by using the warp drive when the velocity vector is drawn towards the black hole to decrease the orbital period and end up with an orbit that would take less than an hour!
Aiming at the other black hole
Now comes the real challenge! Let's say the ship is in an elliptical orbit around an intermediate black hole with an apogee of just a dozen of km/s and a perigee that gets close to the event horizon with a speed of 0.7c. To "slingshot" towards the second black hole, the velocity vector when warp is engaged (this should happen near the perigee) needs to be precisely aligned with the target. This is not easy, as the velocity vector's direction changes rapidly as the ships' orbit progresses at the perigee.
The first thing that needs to be done is make sure the velocity vector's direction gets aligned with the target somewhere near the perigee. There are two necessary steps to do this: first to correct the orbit's inclination to have an alignment somewhere along the orbit, and second to make sure that alignment happens at the perigee. There are no built in tools to do this in the game, but they are two fairly easy steps as only basic orbital mechanics knowledge is needed to achieve them.
For the first step, we can align the part of the orbit trajectory after the perigee with the target icon like this:
To be precise we can zoom in to make sure it is aligned correctly.
For the second step, what is basically needed is the velocity vector to be aligned in a certain direction at the perigee, which means it should be opposite of this direction at the apogee. This part doesn't need to be perfect; even if the alignment happens shorty after or before the perigee, the ship's speed will still be close to the speed of light.
To do this, the ship will need to circle around the black hole using warp until the ship's orbit has the necessary characteristics. Here is a short video of the process: https://youtu.be/7Pj48jsO1wI
At the end of the video, the orbit is ready for the slingshot.
The final part is engaging warp at the perigee as the alignment happens. The easiest way to do it is to slow down time and start the warp engines slowly as the velocity vector aligns, effectively pulling the ship away from the black hole. As the ship loses speed as it leaves the black hole, the velocity vector will slowly align, and when it does completely, we engage warp at full speed. We know we're fully aligned when the warp delta-v approaches its lowest, ideally 0. This process needs to be done efficiently to keep as much of the perigee speed as possible.
Here is another short video of this process: https://youtu.be/a7Qw-zn1sLM
I messed it up a little bit at the end here as I had 400 m/s of warp delta-v, which is already great but could have been brought down to around 60 m/s. This is because warp engines are not instant to power up, which is especially noticeable at slower time speeds and makes the timing more difficult.
And there you go! Now you're on track to going to your target black hole that will help you decelerate to reasonable speeds for interstellar or intergalactic travel!
I may add to this guide the decelerating part of the maneuver in the future, but I hope this helps already and that people interested in this type of maneuver get to see this! I also hope to see some videos of people achieving this, as, as far as I know, it hadn't been done before I did my intergalactic trip video (https://www.youtube.com/watch?v=Swt_ejqYmGM)
I really love Space Engine, as even in this primitive form for the flight simulator, it offers so many possibilities because of its huge universe and realistic physic simulations. Looking forward to seeing many more updates in the years to come, continually improving this truly marvelous piece of art everyone should be aware of!
(if any spelling/grammatical/typos are seen, please tell me! Also, I don't think i'm the best at guides, so if you're having difficulties understanding some parts, tell me and I'll try clearing things up)