Coupled inertial and gravitational effects in the proper reference frame of an accelerated, rotating observer

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Abstract
To the second order in metric and the first order in equations of motion in the local coordinates of an accelerated rotating observer, the inertial effects and gravitational effects are simply additive. To look into the coupled inertial and gravitational effects, we derive the third-order expansion of the metric and the second-order expansion of the equations of motion in local coordinates. Besides purely gravitational (purely curvature) effects, the equations of motion contain, in this order, the following coupled inertial and gravitational effects: redshift corrections to electric, magnetic, and double-magnetic type curvature forces; velocity-induced special relativistic corrections; and electric, magnetic, and double-magnetic type coupled inertial and gravitational forces. An example is provided with a static observer in the Schwarzchild spacetime.

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