I have been thinking about a possible way of exploiting the rotation of a celestial body to accelerate a spacecraft to very high velocities.

The basic idea is:

Instead of trying to accelerate a spacecraft to relativistic speeds entirely with conventional propulsion, could we use the rotational energy and angular momentum of a rapidly rotating celestial body as part of the propulsion system?

The starting point is the familiar relationship:

v = ωr

where ω is the angular velocity and r is the distance from the rotation axis.

On Earth, the surface at the equator already moves at about 465 m/s because of Earth's rotation. If a hypothetical object could remain synchronized with Earth's rotation at a much greater distance from the rotation axis, its tangential velocity would increase proportionally with radius.

This made me wonder whether the same principle could be applied to a much larger or faster-rotating celestial body.

For example, instead of Earth, imagine using something like Jupiter, Saturn, or an extremely rapidly rotating compact object. A spacecraft could theoretically be coupled to a rotating system associated with the body and gain angular momentum from it.

The concept I am imagining is not necessarily a physical cable extending millions of kilometres. That was my original thought, but I realize that such a structure would introduce enormous structural and gravitational problems.

I'm more interested in the underlying question:

Could a physically realizable rotating system around a celestial body transfer enough rotational energy/angular momentum to a spacecraft to produce a substantial fraction of the speed of light?

If so, this could potentially create significant relativistic time dilation for the spacecraft.

For example, if a spacecraft could reach 0.9c, 0.99c, etc., the crew would experience less elapsed time than observers on Earth.

Questions I'm trying to understand

1. Is there a fundamental limit to how much rotational energy/angular momentum could be extracted from a rotating celestial body for spacecraft propulsion?
2. Could a system analogous to a rotovator, momentum-exchange tether, magnetic tether, or other non-rigid structure accomplish something similar without requiring an impossible solid structure?
3. Would a rapidly rotating body such as Jupiter actually be useful for this, or would its gravity and atmospheric environment make the concept impractical?
4. Are there known mechanisms for transferring rotational energy from a planet/star/neutron star to a spacecraft that I should be studying?
5. At what point do orbital mechanics and relativity invalidate the simple v = ωr argument?
6. Could a sufficiently advanced version of such a system theoretically accelerate a spacecraft to, say, 0.5c, 0.9c, or 0.99c?
7. If planets are unsuitable, would rapidly rotating neutron stars or black holes provide a physically meaningful analogue?

I realize there may be obvious problems that I'm overlooking. I'm not claiming that this is a workable time machine. I'm trying to determine whether there is a physically valid propulsion concept hidden in the idea, or whether fundamental physics rules it out.

I'd particularly appreciate explanations involving angular momentum, energy conservation, orbital mechanics, relativistic effects, and structural/engineering constraints.

If there is already an established concept that answers this question, I'd also appreciate being pointed toward it.

Thanks!