Gravitational Cheshire effect: Nonminimally coupled scalar fields may not curve spacetime

TL;DR

This paper demonstrates that nonminimally coupled scalar fields can exist in flat spacetime without causing curvature, revealing a novel gravitational effect called the 'Cheshire effect' that challenges traditional understanding of scalar fields and gravity.

Contribution

It introduces the 'Cheshire effect,' showing scalar fields can be nontrivially configured in flat spacetime due to nonminimal coupling, without affecting spacetime curvature.

Findings

Flat spacetime can host scalar fields satisfying nonlinear Klein-Gordon equations.

The energy-momentum tensor retains a footprint of nonminimal coupling even in flat spacetime.

Solutions include shock waves and instantons, with implications for vacuum states and tachyonic solutions.

Abstract

It is shown that flat spacetime can be dressed with a real scalar field that satisfies the nonlinear Klein-Gordon equation without curving spacetime. Surprisingly, this possibility arises from the nonminimal coupling of the scalar field with the curvature, since a footprint of the coupling remains in the energy-momentum tensor even when gravity is switched off. Requiring the existence of solutions with vanishing energy-momentum tensor fixes the self-interaction potential as a local function of the scalar field depending on two coupling constants. The solutions describe shock waves and, in the Euclidean continuation, instanton configurations in any dimension. As a consequence of this effect, the tachyonic solutions of the free massive Klein-Gordon equation become part of the vacuum.