Emergence of maximal acceleration from non-commutativity of space-time

Abstract

In this paper, we show that the causally connected $4$-dimensional line element of the $\kappa$-deformed Minkowski space-time induces an upper cut-off on the proper acceleration and derive this maximal acceleration, valid up to first order in the deformation parameter. We find a contribution to maximal acceleration which is independent of $\hslash$ and thus signals effect of the non-commutativity alone. We also construct the $\kappa$-deformed geodesic equation and obtain its $\kappa$-deformed Newtonian limit, valid up to first order in deformation parameter. Using this, we constrain non-commutative parameters present in the expression for maximal acceleration. We analyse different limits of the maximal acceleration and also discuss its implication to maximal temperature. We also obtain a bound on the deformation parameter.

arXiv comment14 pages, no figure, Re-wrote Section-4, adding new results. More discussions, two appendices and more references added

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Cited by in corpus (5)

• Maximal acceleration in a Lorentz invariant non-commutative space-time
• Newtonian cosmology and Evolution of kappa-deformed universe
• Entropic force and bouncing behaviour in $\kappa$-Minkowski space-time
• On the Unruh effect for hyperbolic observers in spacetimes of maximal proper acceleration
• Spacetimes of maximal proper acceleration and muon mean lifetime