I'm wondering if a space ship could be accelerated close to the speed of light by putting it in orbit around a black hole and accelerate it externally e.g. with a laser. The idea would be to give it a final push out of orbit such that it would go along some intended linear trajectory close to the speed of light. Might it even be possible to taget another black hole that can "catch" the ship in it's orbit?

What say you good people of SMP?

To hard a question?

If your laser is strong enough to push the ship out of orbit while maintaining a relativistic speed, then you wouldn't need the black hole. Any speed gained from entering orbit will be lost when leaving orbit, all that remains is what is given by the laser. When probes are slingshot around large planets like Jupiter, it's not the gravity that is adding speed to the probe, it's the orbital speed of Jupiter around the sun.

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

Maybe for a rotating black hole, some of the rotational energy of the black hole can be transferred to the ship, not sure.

The Penrose solution for a rotating black hole is well known and it does allow for transfer of energy from the black hole to a ship that enters the ergosphere and makes a proper burn.

Black holes often are misunderstood. People envision a sort of “cosmic vacuum” that just sucks everything in. In reality, at distances far from the Schwarzchild radius (apologies for bad spelling) an observer orbiting a black hole would not notice much difference vs orbiting a regular object with the same mass. For example if the sun were to collapse into a black hole the earth’s orbit would be unaffected. Closer orbits are possible with black holes than regular bodies, so it may be possible to get a relativistic orbital velocity. However a body approaching that closely would already have to be moving at relativistic speed to go into orbit rather than fall into the event horizon, so the black hole can’t be used to generate a relativistic velocity

The other question in all this is deceleration— how do you stop your relativistic spaceship when it reaches its destination?

You take your foot off the gas and coast to a stop.

The idea is not so much to generate the velocity through the black hole, but to keep the space ship more or less in place so that it's easier to accelerate it from the outside. If you externally accelerate a space ship that is constantly moving away from you a lot of energy is lost I would imagine.

I'm not sure about TimM's argument; my naive idea was that you can push the space ship out of orbit with little effort, but that might be wrong since you still have to get out of the gravity well...

This is kinda simple (and again naive): Target another black hole so precisely that the space ship immediately enters its orbit, then decelerate externally!

Orbital stuff is really counterintuitive. And it's worse when you have to consider general relativity and not just use Newtonian mechanics. So strictly Newtonian, say you are in a circular orbit around some body, and want to leave orbit. If you accelerate the ship briefly, you'll go into an elliptical orbit (this is called a transfer orbit). You can then accelerate again to get back into a circular orbit at a larger distance. After accelerating twice, your velocity in the larger circular orbit will be slower than it was in the smaller one! If you do another short acceleration that is enough to reach escape velocity, the orbit becomes parabolic, but you still lose velocity as you get further away.



If you decelerate the ship, you'll fall into the black hole. You have to accelerate to get out of orbit, and when you do, the ship will lose velocity.

So if your small light ship orbiting the black hole is hit with a laser, you will make the orbit more elliptical. You can fix this by having multiple lasers coming from different directions, but accelerating the ship to larger orbits will actually just slow it down. Just hitting the ship will be a challenge, since the laser beam will curve near the black hole. There are other practical problems. Your laser light will be blue-shifted to more energetic wavelengths, and may actually cook the ship you are trying to accelerate.

It's just simpler to skip the black hole stuff, and have a laser at the origin to accelerate the ship and another at the destination to decelerate it.

Ok that makes it even more clear why starting the ship that way doesn't work.

Could you at least use a black hole to "catch" a ship that was accelerated that way? Of course the ship would have to carry the means to get out of the black hole's orbit with it.

No. In the Newtonian gravity approximation you can't even enter an orbit this way. You'll always have escape velocity, even if you did not start with it. The attraction from the large mass will accelerate you above it, and you'll just slingshot past it.

Relativistically, I'm not sure it's possible to enter an orbit that does not spiral into the black hole. There are stable orbits but I'm not sure you can fall into one in the way you describe. If you fall into the Photon sphere you spiral in unless you have enough thrust to escape. If you fall behind the event horizon no amount of thrust will let you escape.

Even if you do fall into a stable orbit (and can somehow survive the tidal forces), your ship will be moving faster than its initial velocity. Remember as you fall closer to the black hole you'll be accelerated by its gravity. Then to get out of that orbit you'll have to accelerate the ship to escape velocity. You'll slow down as you move away, but only as much as you accelerated when falling into the orbit. But you'll still have the same problem in that you will not have lost any of your original speed.