Beyond Analog Gravity: The Case of Exceptional Dynamics

TL;DR

This paper explores how nonlinear dynamics of a self-interacting field can be interpreted as the field influencing itself through an effective metric, extending analog gravity models beyond mere kinematics.

Contribution

It introduces a Lagrangian framework where a field's nonlinear equations of motion are seen as interactions with its own effective metric, advancing the understanding of analog gravity models.

Findings

Demonstrates the possibility of interpreting nonlinear field equations as self-interaction via an effective metric.

Provides a Lagrangian formulation linking field dynamics with an emergent gravitational influence.

Extends the scope of analog gravity models beyond kinematic descriptions.

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. $