  The dual Komar mass generalizes the concept of the NUT parameter and is akin
to the magnetic charge in electrodynamics. In asymptotically flat spacetimes it
coincides with the dual supertranslation charge. The dual mass vanishes
identically on Riemannian manifolds in General Relativity unless conical
singularities corresponding to Misner strings are introduced. In this paper we
propose an alternative way to source the dual mass locally. We show that this
can be done by enlarging the phase space of the theory to allow for a violation
of the algebraic Bianchi identity using local fields. A minimal extension of
Einstein's gravity that meets this requirement is known as the Einstein-Cartan
theory. Our main result is that on Riemann-Cartan manifolds the dual Komar mass
does not vanish and is given by a volume integral over a local 1-form
gravitational-magnetic current that is a function of the torsion.
