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