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We characterize the Casimir forces for the Dirac vacuum on free-fermionicchains with smoothly varying hopping amplitudes, which correspond to (1+1)Dcurved spacetimes with a static metric in the continuum limit. The first-orderenergy potential for an obstacle on that lattice corresponds to the Newtonianpotential associated to the metric, while the finite-size corrections aredescribed by a curved extension of the conformal field theory predictions,including a suitable boundary term. We show that, for weak deformations of theMinkowski metric, Casimir forces measured by a local observer at the boundaryare metric-independent. We provide numerical evidence for our results on avariety of (1+1)D deformations: Minkowski, Rindler, anti-de Sitter (theso-called rainbow system) and sinusoidal metrics.

Casimir forces on deformed fermionic chains