Abstract
We derive bounds on the deformation parameter of the κ-spacetime by analyzing the effect of non-commutativity on astrophysical model. We study compact stars, taken to be degenerate Fermi gas, in non-commutative spacetime. Using tools of statistical mechanics, we derive the degeneracy pressure of the compact star in κ-spacetime and from the hydrostatic equilibrium conditions we obtain a bound on the deformation parameter. We independently derive this bound using generalized uncertainty principle, which is a characteristic feature of quantum gravity approaches, strengthening the bound obtained.
Highlights
Formulating theory of gravitation in the quantum framework is quintessential for a complete understanding of the laws of universe
Since statistical mechanics plays an important role in understanding a system consisting of large number of particles, it is reasonable to assume that a study of statistical mechanics of these compact system in the background of a noncommutative spacetime will be a viable option to understand the Planck scale physics
Compact stars appears to be a potential source to observe the effects of non-commutativity on statistical mechanics, due to its accessibility for observation
Summary
Formulating theory of gravitation in the quantum framework is quintessential for a complete understanding of the laws of universe. It was shown that GUP leads to modification of thermodynamic behavior of these particles [21] This suggest the possibility of studying thermodynamics and statistical mechanics of systems at quantum gravity scales using GUP deformations. In the approach used in this letter, all the effects of κ-deformation is incorporated through the realization of non-commutative coordinates and the corresponding deformed dispersion relation By this approach, we could work with ordinary Fermi statistics for Fermi gas in noncommutative spacetime, expressed in terms of commutative coordinates, their derivatives and deformation parameter a. We could work with ordinary Fermi statistics for Fermi gas in noncommutative spacetime, expressed in terms of commutative coordinates, their derivatives and deformation parameter a With this idea in mind, we use the dispersion relation in this realization to find the density of states for a given energy interval. Using this we obtain a bound on a, which exactly matches with the previously obtained bound
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