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