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

TL;DR

This paper explores how non-commutative geometry affects the maximal acceleration of particles, deriving corrections, equations of motion, and implications for black hole physics and Hawking radiation.

Contribution

It introduces the first-order kappa-deformed corrections to maximal acceleration and geodesic equations, linking non-commutative geometry with gravitational and quantum phenomena.

Findings

Derived kappa-deformed maximal acceleration up to first order.

Established bounds on the deformation parameter from Newtonian limits.

Analyzed modifications to Hawking radiation in non-commutative space-time.

Abstract

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