Newton's Equation on the kappa space-time and the Kepler problem

Abstract

We study the modification of Newton's second law, upto first order in the deformation parameter $a$, in the $\kappa$-space-time. We derive the deformed Hamiltonian, expressed in terms of the commutative phase space variables, describing the particle moving in a central potential in the $\kappa$-space-time. Using this, we find the modified equations of motion and show that there is an additional force along the radial direction. Using Pioneer anomaly data, we set a bond as well as fix the sign of $a$. We also analyse the violation of equivalence principle predicted by the modified Newton's equation, valid up to first order in $a$ and use this also to set an upper bound on $a$.

8 pages, Minor changes in subsection III A made for clarity, to appear in Mod. Phys. Lett. A

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Cited by in corpus (28)

• Electrodynamics on $\kappa$-Minkowski space-time
• Geodesic equation in $k$-Minkowski spacetime
• $\kappa$-deformed Dirac Equation
• Twists, realizations and Hopf algebroid structure of kappa-deformed phase space
• Maxwell's equations on the $\kappa$-Minkowski spacetime and Electric-Magnetic duality
• Uniformly accelerating observer in $\kappa$-deformed space-time
• Hawking radiation in the kappa-spacetime
• Implication of geodesic equation in Generalized Uncertainty Principle framework
• Time-space noncommutativity and Casimir effect
• MICZ Kepler Systems in Noncommutative Space and Duality of Force Laws
• Time varying gravitational constant G via the entropic force
• Closedness of orbits in a space with SU(2) Poisson structure
• Effect of Non-commutativity of space-time on Thermodynamics of Photon gas
• Maximal acceleration in non-commutative space-time and its implications
• Emergence of maximal acceleration from non-commutativity of space-time
• Superdense star in a space-time with minimal length
• Maximal acceleration in a Lorentz invariant non-commutative space-time
• Central force problem in space with SU(2) Poisson structure
• Non-Commutative space-time and Hausdorff dimension
• Newtonian cosmology and Evolution of kappa-deformed universe
• Path integral action of a particle in $\kappa$-Minkowski spacetime
• How does Casimir energy fall in $\kappa$-deformed space-time?
• Generating of additional force terms in Newton equation by twist-deformed Hopf algebras and classical symmetries
• Regularization of Kepler Problem in $\kappa$-spacetime
• Quantisation of $\kappa$-deformed Dirac equation
• Eigenvalue problem for radial potentials in space with SU(2) fuzziness
• Entropic force and bouncing behaviour in $\kappa$-Minkowski space-time
• Maxwell's equations and Lorentz force in doubly special relativity