Equation of motion of a point source of a scalar field in the general theory of relativity

The equation of motion of a point source of a scalar field is derived in the general theory of relativity. The form of this equation is independent of the chosen variant of field equation – with the traditional or with conformally covariant kinetic part. As in the case of an electric charge [2, 10], the source is subject to a force that depends explicitly on the space-time curvature at the position of the source, and this contradicts some formulations of the equivalence principle.