How does Casimir energy fall in $$\kappa $$-deformed space-time?

Abstract

We investigate the response of Casimir energies to fluctuations in a scalar field in the background of a weak gravitational field in $$\kappa $$ κ -deformed space-time. We model the Casimir plates in a gravitational field by $$\kappa $$ κ -deformed Rindler coordinates and calculate the Casimir energy using the $$\kappa $$ κ -deformed scalar field. We show that the Casimir energy accelerates in a weak gravitational field like a mass. Thus, our calculations show that the mass–energy equivalence principle holds in $$\kappa $$ κ -deformed space-time even though a length scale is introduced through space-time non-commutativity.