  We outline the duality between the extraordinary magnetoresistance (EMR),
observed in semiconductor-metal hybrids, and non-symmetric gravity coupled to a
diffusive $U(1)$ gauge field. The corresponding gravity theory may be
interpreted as the generalized complex geometry of the semi-direct product of
the symmetric metric and the antisymmetric Kalb-Ramond field:
($g_{\mu\nu}+\beta_{\mu\nu}$). We construct the four dimensional covariant
field theory and compute the resulting equations of motion. The equations
encode the most general form of EMR within a well defined variational
principle, for specific lower dimensional embedded geometric scenarios. Our
formalism also reveals the emergence of additional diffusive pseudo currents
for a completely dynamic field theory of EMR. The proposed equations of motion
now include terms that induce geometrical deformations in the device geometry
in order to optimize the EMR. This bottom-up dual description between EMR and
generalized geometry/gravity lends itself to a deeper insight into the EMR
effect with the promise of potentially new physical phenomena and properties.
