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The equation of state of the electron degenerate gas in a white dwarf isusually treated by employing the ideal dispersion relation. However, the effectof quantum gravity is expected to be inevitably present and when this effect isconsidered through a non-commutative formulation, the dispersion relationundergoes a substantial modification. In this paper, we take such a modifieddispersion relation and find the corresponding equation of state for thedegenerate electron gas in white dwarfs. Hence we solve the equation ofhydrostatic equilibrium and find that this leads to the possibility of theexistence of excessively high values of masses exceeding the Chandrasekharlimit although the quantum gravity effect is taken to be very small. It is onlywhen we impose the additional effect of neutronization that we obtain whitedwarfs with masses close to the Chandrasekhar limit with nonzero radii at theneutronization threshold. We demonstrate these results by giving the numericalestimates for the masses and radii of $^4He$ and $^{12}C$, and $^{16}O$ whitedwarfs.

Noncommutative dispersion relation and mass-radius relation of white dwarfs