Spinning black holes acting as a slingshot

Question

Could we use spinning black to act as a skyhook giving us enough energy boost to travel the galaxy?

Answer 1

Skyhooks or tethers are most useful for lifting mass from a surface into space, increasing velocity. Kerr blackholes have no appropriate surface for basing mass. Instead a gravity assist maneuver may take advantage of the high spin speed of a Kerr black hole, which induce frame-dragging where the space around the blackhole (within the ergosphere) is dragged at the speed of light in the same direction as the spin.

https://nasa.fandom.com/wiki/Gravity_assist#Limits_to_slingshot_use

The Penrose process also offers a means of extracting energy from Kerr blackholes, if the rotational energy of the black hole is located not inside the event horizon but inside this ergosphere.

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

Answer 2

I recommend you to read the short paper(1) on gravitational machines by late physicist Freeman Dyson. As Dyson puts it:

The difficulty in building machines to harness the energy of the gravitational field is entirely one of scale. Gravitational forces between objects of a size that we can manipulate are so absurdly weak that they can be scarcely be measured, let alone exploited. To yield a useful output of energy, any gravitational machine must be built on a scale that is literally astronomical.

Black holes aren't necessary, you could actually do the trick with binary stars, like white dwarfs. A pair to accelerate your payload, and another to decelerate it at destination.

A double star has two components A and B, each with mass M, revolving around each other in a circular orbit of radius R. The velocity of each star is $$V = \sqrt \frac{GM}{4R}$$ where $$G = 6.7*10^{-8} > cm^3/sec^2g$$ is the gravitational constant. The exploiters of the device are living on a planet or vehicle P which circles around the double star at a distance much greater than R. They propel a small mass C into a orbit which fall toward the double star, starting from P with a small velocity. The orbit of C is computed in such a way that it makes a close approach to B at a time when B is moving in a direction opposite to the direction of arrival of C. The mass C then swings around B and escapes with greatly increased velocity. The effect is almostif the light mass C had made a elastic collision with the moving heavy mass B. The mass C will arrive at a distant point Q with velocity somewhat greater than 2V. At Q the mass C may be intercepted and its kinetic energy converted into useful form. Alternatively the device may be used as a propulsion system, in which case C merely proceeds with velocity 2V to its destination. The destination might be a similar device situated very far away, which brings C to rest by the same mechanism working in reverse.

Dyson estimates that a white dwarf version of this device could accelerate a payload to about 2000 km/sec.

The main limitations on this method, beyond the sheer scale involved, are tidal stresses on larger payloads, given the accelerations involved, and the suitable systems are quite short-lived, decaying due to gravitational radiation.

(1). Dyson, F. (1963). Gravitational machines. Interstellar Communication, edited by AGW Cameron,(Benjamin Press, New York, 1963).