# Black hole slingshot?

Gravitational slingshot of light using a black hole/massive object

But that is talking about photons around a black hole.

Now I am interested in macro objects. I would like to know if a spaceship can theoretically use a black hole for a slingshot.

Spaceships can even with nowadays technology do slingshots around Jupiter.

I was wondering if they can do theoretically the same slingshot around a black hole?

Question:

1. Can a spaceship theoretically use a black hole for a slingshot?
• Isn't this question essentially the same as all the questions asking what would happen if the sun (or any other object in space) suddenly became a black hole? At any significant distance, the gravitational fields would be unaffected. – D. Halsey Sep 23 '18 at 17:58

The answer is trivially yes: if you can do a slingshot around, say, the Sun, you can do it around a black hole, because the far field of a BH is the same as the far field of any other massive object.

The interesting question is whether there are tricks you can do by passing rather close to the event horizon: I'm not sure but I suspect there are not any easy ones, or possibly any, because slingshots are not extracting energy from the object itself but rather from its translational kinetic energy (in Newtonian terms).

There is one thing you can do with a spinning BH, which is called the Penrose process. This is not a slingshot but involves throwing part of your mass into the BH and extract some of its rotational momentum.

We have to distinguish between a passive gravity assist and an active one using the Oberth effect.

The question you linked to is about passive gravity assists. In this situation, the math is the same for a black hole as for any other object, because it's just a matter of velocity addition. If the speeds are relativistic, then you have to use special-relativistic velocity addition. In the simplest case, where the scattering is at 180 degrees, you just need one-dimensional velocity addition. You don't need any general relativity, basically because the spacetime is asymptotically flat and the initial and final states have the spacecraft at infinity. The only difference between the case of a black hole and that of any other body is that a black hole is able to effect, e.g., a 180-degree course change for a spacecraft that is moving at highly relativistic speeds, whereas for a less compact orbit that wouldn't work.

The Oberth effect with a black hole might in principle allow extremely impressive maneuvers. Nonrelativistically, the effect comes about because work goes like $$F\cdot v$$, and $$v$$ can be very large at periapsis. Relativistically, the details will be different, but we would basically expect an analogous effect, and it could be large because $$v$$ can be so large.

I'm giving you a short and simple answer:

As already mentioned by @D.Halsey in the comment above that, it does't matter whether your doing a slingshot around a black hole or a massive object like dead star or a hypothetical giant massive object, what matters is that how strong is the gravitational field of that object(spacetime curvature around the object) and the surrounding.

Assuming simplest Swarzschild's black hole:

If your spaceship can achieve enormous speeds then theoritically you can slingshot just like jupiter's case but there will be additional consequences of gravitational plus relativistic time dilations.

For a non-spinning (or slowly spinning) black hole with zero (or minimal) charge, we can evaluate the trajectory using the Schwarzschild metric. A black hole can be used to slingshot around just like any massive object. But the Schwarzschild metric indicates 3 notes of caution:

1. There are no stable (circular) orbits below 3 times the Schwarzschild radius. Below that level, you would spiral into the black hole. Even light can only orbit at 1.5 times the Schwarzchild radius.

2. The Schwarzschild radius is measured as the circumference divided by 2 * pi, not the actual radial distance.

3. The tidal forces from a black hole might destroy your craft by stretching and squeezing, even if past 3 times the Schwarzschild radius for a smaller black hole.

All that to say, a black hole can be used to slingshot around, but don't get too close!

• There are no stable (circular) orbits below 3 times the Schwarzschild radius. Below that level, you would spiral into the black hole. The second sentence is not true. We can have scattering trajectories than reach periastron at any radius greater than the Schwarzschild radius. The Schwarzschild radius is measured as the circumference divided by 2 pi, not the actual radial distance. True, but why would this be relevant? – user4552 Sep 24 '18 at 0:39
• @BenCrowell "Below that level, you would spiral into the black hole. The second sentence is not true." I suppose that is true for a slingshot with added power (thrust). I was thinking more in terms of an orbit without thrust where I believe 3*Rs is the minimum radius. – Stuart Van Horne Sep 24 '18 at 19:52
• @BenCrowell As for the Schwarzschild coordinate system, I have found that most commentators treat it as some kind of fixed distance, as if you could lower something to it with an infinitely strong cable. If I read the Schwarzschild metric correctly, it is an infinite coordinate distance to Rs from any stationary (comoving) position outside of Rs. Feedback appreciated. – Stuart Van Horne Sep 24 '18 at 20:02