Emergence of maximal acceleration from non-commutativity of spacetime

Abstract

In this paper, we show that the causally connected four-dimensional line element of the κ-deformed Minkowski spacetime 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 and thus signals effect of the non-commutativity alone. We also construct the κ-deformed geodesic equation and obtain its κ-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 analyze different limits of the maximal acceleration and also discuss its implication to maximal temperature. We also obtain a bound on the deformation parameter.