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 φ as an interaction between φ and its associated effective metric gμν . In other words, the nonlinear equation of motion of the field may be interpreted as the gravitational influence on φ by its own effective metric which, in our scheme, becomes an active partner of the dynamics of φ.
Authors: M Novello and E Goulart.