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 a weak gravitational field in the $\kappa$-deformed space-time. We model the Casimir plates in a gravitational field by $\kappa$-deformed Rindler coordinates and calculate the Casimir energy using the $\kappa$-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 $\kappa$-deformed space-time even though a length scale is introduced through space-time non-commutativity.

24 pages

References in corpus (14)

• A Gravity Theory on Noncommutative Spaces
• Kappa-Minkowski space-time and the star product realizations
• New realizations of Lie algebra kappa-deformed Euclidean space
• How Does Casimir Energy Fall?
• Covariant realizations of kappa-deformed space
• How does Casimir energy fall? II. Gravitational acceleration of quantum vacuum energy
• Newton's Equation on the kappa space-time and the Kepler problem
• Newton equation for canonical, Lie-algebraic and quadratic deformation of classical space
• Boundaries and the Casimir effect in non-commutative space-time
• Energy-momentum tensor of a Casimir apparatus in a weak gravitational field: scalar case
• How does Casimir energy fall? III. Inertial forces on vacuum energy
• Casimir effect in 2+1 dimensional noncommutative theories
• Superdense star in a space-time with minimal length
• Casimir effect in DFR space-time

Cited by in corpus (2)

• Centripetal force on Casimir energies in $\kappa$-deformed rotating frame
• Thermal Casimir effect in $\kappa$-Minkowski space-time