Maximal acceleration in non-commutative space–time and its implications

Abstract

In this paper, we derive the non-commutative corrections to the maximal acceleration of a massive particle. Using the eight-dimensional κ-deformed phase-space metric, we obtain the κ-deformed maximal acceleration, valid up to first order in the deformation parameter. We then derive the κ-deformed geodesic equation and obtain its Newtonian limit and from this obtain a bound on the deformation parameter. After re-expressing the κ-deformed Schwarzschild metric in terms of maximal acceleration, we analyse the motion of a particle in this space–time, and also study the modifications to Hawking radiation. We also derive the κ-deformed corrections to maximal acceleration using κ-deformed generalised uncertainty principle.