We know GR turns gravitation induced acceleration into curvature in spacetime. But in GR, what happens to the acceleration due to the centrifugal force? And similarly, the acceleration due Euler or Coriolis force?
The law of inertia can be stated by saying that the covariant derivative of the velocity vector is zero for a free particle. The covariant derivative with respect to a certain coordinate differs from the partial derivative by a term involving a Christoffel symbol. In a rotating coordinate system, these terms can be interpreted as describing the centrifugal and Coriolis forces. No curvature is involved, so this is not really GR.
The answer by Constantin is wrong. His example of the bike inside the cylinder presupposes a centripetal force, but we can observe the centrifugal and Coriolis forces regardless of whether there is a centripetal force. The centrifugal and Coriolis forces exist in any rotating coordinate system.
If the movement is due to a gravitational phenomenon then the particle will "fall" along a geodesic trajectory and the study of this trajectory will describe the movement and will take care of what we experience as acceleration and therefore forces on the object. You would need to use the geodesics to calculate how we can experience that as a centripetal force or any other (it GR is more complicated and there are other phenomena such as frame dragging problems). For Example, you can check the calculation for a "free" moving object in a Schwarzschild space-time, along the geodesics, and recover the planetary or any other conic trajectory and even profound non-Newtonian corrections. If you want to consider Coriolis you would need to use a more complicated metric. In this free article you find discussions which might help with this: