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In a scalar-tensor theory of gravity we consider a global monopole field as a candidate for galactic dark matter. Within the weak gravity approximation we solve the equations of a metric tensor and a scalar field coupled to the monopole and determine the asymptotic structure of a galactic spacetime for large r. In the case of a massless scalar field, we derive a formula for the rotation velocity of stars, which contains an extra constant value in addition to the other known terms, and we discuss its relation to flat rotation curves in the galaxy.
Lee et al. (Fri,) studied this question.