  Recently it was suggested that the Unruh effect might occur in metamaterials
at accessible Unruh temperatures. In some cases, the class of metamaterials
that may be useful for this observation has a Klein instead of a Minkowski
signature. Thus, confirmation of this effect in those materials requires more
careful analysis. In this paper, we use the path integral formulation of
Quantum Field Theory to investigate the analogous to the Unruh effect in
Kleinian geometry. We calculate the analogous of the Unruh temperature for a
scalar theory, provided we restrict the action in a convenient subspace of the
Kleinian spacetime. As a consequence, we obtain the diamond temperature for a
static observer with a finite lifetime. The result suggest metamaterials as a
possible system to observe diamond regions.
