Geodesic equation in $k$-Minkowski spacetime

Abstract

In this paper, we derive corrections to the geodesic equation due to the $k$-deformation of curved space-time, up to the first order in the deformation parameter a. This is done by generalizing the method from our previous paper [31], to include curvature effects. We show that the effect of $k$-noncommutativity can be interpreted as an extra drag that acts on the particle while moving in this $k$-deformed curved space. We have derived the Newtonian limit of the geodesic equation and using this, we discuss possible bounds on the deformation parameter. We also derive the generalized uncertainty relations valid in the non-relativistic limit of the $k$-space-time.

11 pages, references added

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• Twists, realizations and Hopf algebroid structure of kappa-deformed phase space
• Effects of Noncommutativity on the Black Hole Entropy
• Noncommutative correction to the entropy of Schwarzschild black hole with GUP
• $\kappa$-Deformed Phase Space, Hopf Algebroid and Twisting
• Quantum mechanics with coordinate dependent noncommutativity
• Uniformly accelerating observer in $\kappa$-deformed space-time
• $\kappa$-Deformations and Extended $\kappa$-Minkowski Spacetimes
• Universal $\kappa$-Poincaré covariant differential calculus over $\kappa$-Minkowski space
• Differential forms and k-Minkowski spacetime from extended twist
• Hawking radiation in the kappa-spacetime
• Hermitian realizations of kappa-Minkowski spacetime
• Uniformly accelerated detector in the $\kappa$-deformed Dirac vacuum
• Implication of geodesic equation in Generalized Uncertainty Principle framework
• Generalized Heisenberg algebra applied to realizations of the orthogonal, Lorentz and Poincare algebras and their dual extensions
• Quantisation of Klein-Gordon field in $\kappa$ space-time: deformed oscillators and Unruh effect
• MICZ Kepler Systems in Noncommutative Space and Duality of Force Laws
• Central tetrads and quantum spacetimes
• Emergence of maximal acceleration from non-commutativity of space-time
• Two-particle system in Coulomb potential for twist-deformed space-time
• Poisson electrodynamics on $\kappa$-Minkowski space-time
• Non-Commutative space-time and Hausdorff dimension
• Regularization of Kepler Problem in $\kappa$-spacetime
• Superradiance scattering of scalar, electromagnetic, and gravitational fields and thin accretion disk around non-commutating Kerr black hole
• Neutron Star in Quantized-space-time
• Quantisation of $\kappa$-deformed Dirac equation
• Influence of the cosmological constant on $\kappa$-deformed Neutron Star
• Wormhole Solutions in deformed space-time
• Non-commutative correction of ideal gas thermodynamics
• Entropic force and bouncing behaviour in $\kappa$-Minkowski space-time
• On interpolations between Jordanian twists
• Maxwell's equations and Lorentz force in doubly special relativity
• Twist deformations of Newtonian Schwarzschild-(Anti-)de Sitter classical system
• Effect of Noncommutativity of Space-time on Zitterbewegung
• Fradkin-Bacry-Ruegg-Souriau vector in kappa-deformed space-time