## geodesics in a rotating coordinate system

In a uniformly rotating coordinate system the trajectories of freely moving objects are influenced by an apparent centrifugal and Coriolis force. Is there a coordinate system or metric (or both) in which these trajectories are geodesics instead?
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 Quote by snoopies622 In a uniformly rotating coordinate system the trajectories of freely moving objects are influenced by an apparent centrifugal and Coriolis force. Is there a coordinate system or metric (or both) in which these trajectories are geodesics instead?
The property of being a geodesic doesn't depend on the coordinate system. The trajectories of freely moving objects are always geodesics, whatever coordinate system you use.

In non-rotating Cartesian coordinates $x = vt$ is a geodesic, which in rotating Cartesian coordinates might become $X \cos \omega T + Y \sin \omega T = VT$. In these coordinates $X = VT$ would not be a geodesic.

 Recognitions: Science Advisor Staff Emeritus The trajectories of freely moving objects will be geodesics in any coordinate system. The condition for a path being a geodesic is that there are no "real" forces influencing the path. In an inertial frame, there are no real and no apparent forces on a geodesic trajectory. In a non-inertial frame, such as your rotating frame, there may be apparent forces on a geodesic trajectory, but there are still no "real" forces.