Hidden geometries in nonlinear theories: a novel aspect of analogue gravity

TL;DR

This paper demonstrates that nonlinear scalar field dynamics can be interpreted as modifications to spacetime geometry, revealing a universal coupling with an effective metric constructed from the field itself, extending analogue gravity models.

Contribution

It introduces a universal framework where nonlinear scalar fields modify spacetime geometry, generalizing previous linear perturbation-based analogue gravity models.

Findings

Nonlinear scalar fields can be described as coupling to an effective metric.

The process is universal for arbitrary Lagrangians.

Comparison with linear analogue models highlights new geometric insights.

Abstract

We show that non-linear dynamics of a scalar field {\phi} may be described as a mod- ification of the spacetime geometry. Thus, the self-interaction is interpreted as a coupling of the scalar field with an effective gravitational metric that is constructed with {\phi} itself. We prove that this process is universal, that is, it is valid for arbi- trary Lagrangian. Our results are compared to usual analogue models of gravitation, where the emergence of a metric appears as a consequence of linear perturbation.