Here's a simplified explanation.

Newton's Bucket is a thought experiment proposed by Isaac Newton, which he used to demonstrate the existence of absolute space. He imagined a bucket filled with water suspended by a cord. If the bucket is twisted, and then released, it begins to spin. As the bucket spins, the water inside it climbs up the sides, forming a concave surface. Newton argued that this change in the water's shape was due to its rotation relative to absolute space. Ernst Mach, a 19th-century physicist and philosopher, offered a different viewpoint. He suggested that instead of absolute space - the bucket can be seen as stationary while the universe is rotating, and the water would also have the same concave surface. This is known as Mach's Principle. According to General Relativity, a rotating universe can actually "drag" the space and time in it, affecting the spacetime of the bucket, so there doesn't need to be any centrifugal forces. This omits the need for any "absolute rotation" or "absolute coordinates".

But your question is about whether there can be centrifugal force in a non-rotating system.

There are black holes that aren't rotating.

Godel's dust fluid solutions to Relativity eventually satisfied the prevailing criteria of cosmological expansion and rotation.

Centrifugal force: https://en.wikipedia.org/wiki/Centrifugal_force

Inertial frame of reference: https://en.wikipedia.org/wiki/Inertial_frame_of_reference

If there are no straight-line paths through spacetime which is necessarily curved if there is mass inertia to describe, aren't most spacetime paths relatively curved and is that rotation?

All transformations in Minkowski space-time are rotations in space-time.

Geodesics in general relativity: https://en.wikipedia.org/wiki/Geodesics_in_general_relativit... :

> In Minkowski space there is only one geodesic that connects any given pair of events, and for a time-like geodesic, this is the curve with the longest proper time between the two events. In curved spacetime, it is possible for a pair of widely separated events to have more than one time-like geodesic between them. In such instances, the proper times along several geodesics will not in general be the same. For some geodesics in such instances, it is possible for a curve that connects the two events and is nearby to the geodesic to have either a longer or a shorter proper time than the geodesic. [11]

In superfluid spacetime, n-body gravity is most correctly predicted by a fluidic or a dust model with vorticity; which is a like rotation.

/? Vorticity curl: https://www.google.com/search?q=vorticity+curl :

- "Vorticity dynamics" (2016) https://www.researchgate.net/publication/300133454_Vorticity... :

> The vorticity field is the curl of the velocity field, and is twice the rotation rate of fluid particles. The vorticity field is a vector field, and vortex lines may be determined from a tangency condition similar to that relating streamlines to the fluid velocity field. However, vortex lines have several special properties and their presence or absence within a region of interest may allow certain simplifications of the field equations for fluid motion. In particular, vortex lines are carried by the flow and cannot end within the fluid, and this constrains their possible topology. Vorticity is typically present at solid boundaries and it may diffuse into the flow via the action of viscosity. Vorticity may be generated within a flow wherever there is an unbalanced torque on fluid elements, such as when pressure and density gradients are misaligned. The characteristics and geometry of a vortex line allow the velocity it induces at a distant location to be determined. Thus, multiple vortex lines that are free to move within a fluid may interact with each other. In a rotating coordinate frame, the observed vorticity depends or the frame's rotation rate.