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

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

2010-03-24

arxiv.org/abs/1003.4603v3

Mod.Phys.Lett.A25:2991-3002,2010

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1142/S021773231003416X

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 $a$.

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