Gravitational Cheshire effect: Nonminimally coupled scalar fields may not curve spacetime
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.
Keywords
Cite
@article{arxiv.hep-th/0505086,
title = {Gravitational Cheshire effect: Nonminimally coupled scalar fields may not curve spacetime},
author = {Eloy Ayón-Beato and Cristián Martínez and Ricardo Troncoso and Jorge Zanelli},
journal= {arXiv preprint arXiv:hep-th/0505086},
year = {2007}
}
Comments
8 pages, 1 figure, CECS style; small changes to match published version, title changed by journal