Effective metric in nonlinear scalar field theories

TL;DR

This paper explores how perturbations propagate in nonlinear scalar field theories through the effective metric, classifying propagation based on the scalar field's gradient and illustrating the diversity of effective metric signatures.

Contribution

It introduces a classification scheme for the effective metric in nonlinear scalar theories based on the scalar field gradient and demonstrates the possibility of different metric signatures.

Findings

Effective metric classification depends on the scalar field gradient.

Different signatures for the effective metric are possible.

Illustrative examples demonstrate the classification scheme.

Abstract

We discuss several features of the propagation of perturbations in nonlinear scalar field theories using the effective metric. It is shown that the effective metric can be classified according to whether the gradient of the scalar field is timelike, null, or spacelike, and this classification is illustrated with two examples. We shall also show that different signatures for the effective metric are allowed.