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.

arXiv comment24 pages

References in corpus (42)

• String Theory and Noncommutative Geometry
• Noncommutative Field Theory
• Quantum Field Theory on Noncommutative Spaces
• Bicrossproduct structure of $\kappa$-Poincare group and non-commutative geometry
• On a Lorentz-Invariant Interpretation of Noncommutative Space-Time and Its Implications on Noncommutative QFT
• A Gravity Theory on Noncommutative Spaces
• The Casimir effect: Recent controversies and progress
• Emergence of a 4D World from Causal Quantum Gravity
• Classical and Quantum Mechanics of Free \k Relativistic Systems
• Noncommutative Geometry and Gravity
• 3d Quantum Gravity and Effective Non-Commutative Quantum Field Theory
• Introduction to Doubly Special Relativity
• Deformed Field Theory on kappa-spacetime
• Kappa-Minkowski space-time and the star product realizations
• New realizations of Lie algebra kappa-deformed Euclidean space
• How Does Casimir Energy Fall?
• Comments on the Hydrogen Atom Spectrum in the Noncommutative Space
• Covariant realizations of kappa-deformed space
• Electrodynamics on $\kappa$-Minkowski space-time
• Energy-momentum tensor for a Casimir apparatus in a weak gravitational field
• Constraints on the quantum gravity scale from kappa - Minkowski spacetime
• Vacuum fluctuation force on a rigid Casimir cavity in a gravitational field
• Symmetries of quantum space-time in 3 dimensions
• How does Casimir energy fall? II. Gravitational acceleration of quantum vacuum energy
• Kappa-Minkowski spacetime, Kappa-Poincaré Hopf algebra and realizations
• Newton's Equation on the kappa space-time and the Kepler problem
• Noncommutative scalar quasinormal modes and quantization of entropy of a BTZ black hole
• $\kappa$-deformed Dirac Equation
• Newton equation for canonical, Lie-algebraic and quadratic deformation of classical space
• How does Casimir energy fall? IV. Gravitational interaction of regularized quantum vacuum energy
• Boundaries and the Casimir effect in non-commutative space-time
• How does Casimir energy fall? III. Inertial forces on vacuum energy
• Energy-momentum tensor of a Casimir apparatus in a weak gravitational field: scalar case
• Casimir effect in free-fall towards a Schwarzschild black hole
• Null Second Order Corrections to Casimir Energy in Weak Gravitational Field
• Hawking radiation in the kappa-spacetime
• Kappa-deformed quantum field theory and Casimir effect
• Casimir effect in 2+1 dimensional noncommutative theories
• Compact stars in quantum spacetime
• Time-space noncommutativity and Casimir effect
• Superdense star in a space-time with minimal length
• Casimir effect in DFR space-time

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