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

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 $\hbar$ 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.