  We review the hypothesis of the existence of gravitational magnetic monopoles
(H-pole for short) defined in analogy with the Dirac's hypothesis of magnetic
monopoles in electrodynamics. These hypothetical dual particles violate the
equivalence principle and are accelerated by a gravitational field. We propose
an expression for the gravitational force exerted upon an H-pole. According to
GR ordinary matter (which we call E-poles) follows geodesics in a background
metric. The dual H-poles follows geodesics in an effective metric.
