On symmetry inheritance of nonminimally coupled scalar fields

TL;DR

This paper investigates how nonminimally coupled scalar fields, specifically with a $\xi\phi^2 R$ interaction, can either inherit or break spacetime symmetries, providing classifications and examples of such configurations.

Contribution

It is the first analysis of symmetry inheritance for nonminimally coupled scalar fields, classifying potentials that allow stealth configurations on Einstein solutions.

Findings

Identifies conditions under which scalar fields inherit or break symmetries.

Classifies scalar potentials permitting stealth configurations.

Provides examples of symmetry noninheriting scalar fields in Einstein spacetimes.

Abstract

We present the first symmetry inheritance analysis of fields nonminimally coupled to gravity. In this work we are focused on the real scalar field $\phi$ with nonminimal coupling of the form $\xi\phi^2 R$. Possible cases of the symmetry noninheriting fields are constrained by the properties of the Ricci tensor and the scalar potential. Examples of such spacetimes can be found among those which are "dressed" with the stealth scalar field, a nontrivial scalar field configuration with the vanishing energy-momentum tensor. We classify the scalar field potentials which allow the symmetry noninheriting stealth field configurations on top of the exact solutions of the Einstein's gravitational field equation with the cosmological constant.