Narrow Results

In this paper, we generalize core–envelope model of superdense star to a noncommutative spacetime and study the modifications due to the existence of a minimal length, predicted by various approaches to quantum gravity. We first derive Einstein’s field equation in $\kappa$-deformed spacetime and use this to set up noncommutative version of core–envelope model describing superdense stars. We derive $\kappa$-deformed law of density variation, valid up to first-order approximation in deformation parameter and obtain radial and tangential pressures in $\kappa$-deformed spacetime. We also derive $\kappa$-deformed strong energy conditions and obtain a bound on the deformation parameter.

In this paper, we show that the causally connected four-dimensional line element of the $\kappa$-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 $\hslash$ and thus signals effect of the non-commutativity alone. We also construct the $\kappa$-deformed geodesic equation and obtain its $\kappa$-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.