Non-Noetherian conformal Cheshire effect

TL;DR

This paper explores the gravitational Cheshire effect in a broad class of conformal scalar field theories, revealing new flat spacetime solutions that demonstrate nonminimal coupling effects without backreaction.

Contribution

It fully characterizes spherically symmetric stealth solutions in a general non-Noetherian conformal scalar field theory, including a novel solution branch enabled by non-Noetherian contributions.

Findings

Identified two solution branches: standard and non-Noetherian.

Derived a nonlinear PDE governing the new branch.

Provided the general solution using advanced mathematical methods.

Abstract

The gravitational Cheshire effect refers to the possibility of turning off the gravitational field while still leaving an imprint of the nonminimal coupling of matter to gravity. This allows nontrivial solutions in flat spacetime for which no backreaction is possible. The effect was originally shown to manifest itself for standard nonminimal couplings, such as those allowing conventional conformally invariant scalar fields. Recently, the most general scalar field action yielding a conformally invariant second-order equation was constructed, and entails a more involved nonminimal coupling explicitly breaking the conformal invariance of the action without spoiling it in the equation. We have succeeded in fully describing the spherically symmetric stealth solutions on flat spacetime supporting the Cheshire effect within this general non-Noetherian conformal theory. The allowed configurations are divided into two branches: The first one essentially corresponds to an extension of the solutions already known for the standard Noetherian conformal theory. The second branch is only possible due to the non-Noetherian conformal contribution of the action. The complete characterization of this branch is expressed by a nonlinear first-order partial differential equation. We have found the general solution of this equation using both seemingly new and well-established mathematical tools.