  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.
