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

Eloy Ayón-Beato·Cristián Martínez·Ricardo Troncoso·Jorge Zanelli
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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.

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Eloy Ayón-Beato, Cristián Martínez, Ricardo Troncoso, Jorge Zanelli. 2005-06-07. Gravitational Cheshire effect: Nonminimally coupled scalar fields may not curve spacetime. https://doi.org/10.1103/physrevd.71.104037

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