Beyond analog gravity: the case of exceptional dynamics

Abstract

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