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We investigate the response of Casimir energies to fluctuations in a scalar field in a weak gravitational field in the κ-deformed space-time. We model the Casimir plates in a gravitational field by κ-deformed Rindler coordinates and calculate the Casimir energy using the 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 κ-deformed space-time even though a length scale is introduced through space-time non-commutativity.
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Harikumar et al. (2024) studied this question.
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