Newtonian analogue of force and motion of a free particle in the graviational field of the C-metric (Q1115662)

The Newtonian analogue of force for the C-metric has been investigated. To the first-order of approximation in the absence of acceleration of the particle generating the C-metric, one component of the force vector corresponds to the Newtonian analogue of force. In general there are relativistic correction terms due to acceleration term in the C-metric. The motion of a freely falling body has been investigated. It is found that plane orbits are not possible. Also the radial fall is not possible and in the equation of the orbit there are terms having no classical analogue. They can be interpreted as the effect of the dragging of the inertial frame produced by the rectilinear acceleration.