Casimir effect in Post-Newtonian gravity with Lorentz-violation

We study the Casimir effect in the framework of standard model extension. Employing the weak field approximation, the vacuum energy density $$\varepsilon $$ and the pressure for a massless scalar field confined between two nearby parallel plates in a static spacetime background are calculated. In addition, through the analysis of $$\varepsilon $$, we speculate a plausible constraint on the Lorentz-violating term $${\bar{s}}^{\,00}$$ which is lower than the bounds currently available for this quantity. Finally, we remark that our outcome has an intrinsic validity that goes beyond the treated case of a point-like source of gravity