Beyond analog gravity: the case of exceptional dynamics

We show that it is possible to go beyond the propagation aspects usually contemplated in the analog models of gravity. Until now, the emergence of a metric appears in the description of excitations around a given background solution or in the study of field discontinuities in the geometrical optics regime. We now overcome some limitations of the above analogies and exhibit the form of a Lagrangian that describes the dynamics of a self-interacting field phi as an interaction between phi and its associated effective metric (g) over cap (mu nu). In other words, the nonlinear 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.