Beyond Analog Gravity: The Case of Exceptional Dynamics

Abstract: We show that it is possible to go beyond the simple kinematical aspects of the analog models of gravity. We exhibit the form of the Lagrangian that describes the dynamics of a self-interacting field $ \phi $ as an interaction between $ \phi $ and its associated effective metric $ \hat{g}^{\mu\nu}.$ In other words the non-linear equation of motion of the field may be interpreted as the gravitational influence on $ \phi $ by its own effective metric which, in our scheme becomes an active partner of the dynamics of $ \phi. $