https://doi.org/10.1140/epjp/s13360-022-03195-4
Regular Article
Maximal acceleration in a Lorentz invariant non-commutative space-time
School of Physics, University of Hyderabad, Central University P.O, 500046, Hyderabad, Telangana, India
Received:
6
July
2022
Accepted:
13
August
2022
Published online:
26
August
2022
In this paper, we derive the non-commutative corrections to the maximal acceleration in the Doplicher–Fredenhagen–Roberts (DFR) space-time and show that the effect of the non-commutativity is to decrease the magnitude of the value of the maximal acceleration in the commutative limit. We also obtain an upper bound on the acceleration along the non-commutative coordinates using the positivity condition on the magnitude of the maximal acceleration in the commutative space-time. From the Newtonian limit of the geodesic equation and Einstein’s equation for linearised gravity, we derive the explicit form of Newton’s potential in DFR space-time. By expressing the non-commutative correction term of the maximal acceleration in terms of Newton’s potential and applying the positivity condition, we obtain a lower bound on the radial distance between two particles under the gravitational attraction in DFR space-time. We also derive modified uncertainty relation and commutation relation between coordinates and its conjugate, due to the existence of maximal acceleration.
Suman Kumar Panja and Vishnu Rajagopal are equally contributed to this work.
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