2021
DOI: 10.1142/s0217732321500693
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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 [Formula: see text]-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 [Formula: see text] and thus signals effect of the non-commutativity alone. We also construct the [Formula: see text]-deformed geodesic equation and obtain its [Fo… Show more

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Cited by 4 publications
(4 citation statements)
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“…α, β, and γ are real constants with γ = 1 + α. In order to avoid the Hamiltonian/Lagrangian for simple models with explicit time dependence and to obtain the proper commutative limit (deformation parameter, a → 0), we set β = 0 (for details, see discussion in [28,50]).…”
Section: α β and γ-Realizationmentioning
confidence: 99%
See 1 more Smart Citation
“…α, β, and γ are real constants with γ = 1 + α. In order to avoid the Hamiltonian/Lagrangian for simple models with explicit time dependence and to obtain the proper commutative limit (deformation parameter, a → 0), we set β = 0 (for details, see discussion in [28,50]).…”
Section: α β and γ-Realizationmentioning
confidence: 99%
“…In Figure 4, we have plotted the variation of the scale factor A ± for the matterdominated universe for both the commutative case and non-commutative corrected case (Equation ( 55)), with τ. Taking the same numerical values for m (mass of Andromeda galaxy) and p 0 (obtained from black hole mass) as before, and using α = − 3 4 [50], we find the bound for the deformation parameter a as |a| ≤ 10 −85 m. From the Figure 4, we find that for α, β, and γ realizations in the case of the radiation-dominated flat universe, the curves show similar behavior as in the spatially flat, radiation-dominated case (discussed in Section 4.1.1) depending on the sign of deformation parameter a.…”
Section: For α β and γ-Realizationmentioning
confidence: 99%
“…The existence of a maximal acceleration has been a matter of research for a long time in different contexts. Starting as a consequence of Caianiello's quantum geometry, [6], it has been a recurrent topic in field theory [5], in string field theory [8,23], loop quantum gravity [25], non-commutative spacetimes [18,19,17] or classical electrodynamics [7,26,10,12,13]. Different faces of maximal acceleration have been also reviewed in [14].…”
Section: Introductionmentioning
confidence: 99%
“…The MA has been shown to exist in the covariant loop quantum gravity model [16]. The emergence of MA has also been shown from the causally connected line element in κ-Minkowski space-time [17]. The MA in commutative space-time has been obtained by incorporating the notion of quantum mechanics into the 8-dim phase-space of a massive particle [18].…”
Section: Introductionmentioning
confidence: 99%