Noncommutative dispersion relation and mass-radius relation of white dwarfs

Abstract

The equation of state of the electron degenerate gas in a white dwarf is usually treated by employing the ideal dispersion relation. However, the effect of quantum gravity is expected to be inevitably present and when this effect is considered through a non-commutative formulation, the dispersion relation undergoes a substantial modification. In this paper, we take such a modified dispersion relation and find the corresponding equation of state for the degenerate electron gas in white dwarfs. Hence we solve the equation of hydrostatic equilibrium and find that this leads to the possibility of the existence of excessively high values of masses exceeding the Chandrasekhar limit although the quantum gravity effect is taken to be very small. It is only when we impose the additional effect of neutronization that we obtain white dwarfs with masses close to the Chandrasekhar limit with nonzero radii at the neutronization threshold. We demonstrate these results by giving the numerical estimates for the masses and radii of 4 2 He and 12 6 C, and 16 8 O white dwarfs. * a.mathew@iitg.ac.in † mknandy@iitg.ac.in

Prospect of Chandrasekhar's limit against modified dispersion relation

“…The problem thus calls for taking account of the effect of quantum space-time fluctuations at ultrahigh densities of the electron degenerate gas. When this notion is followed and the electron gas is treated via a modified dispersion relation making the equation of state more stiff than the ideal one, it is found that white dwarfs become "super-stable" and higher masses beyond the Chandrasekhar limit are possible [4] when the gravity is treated in the Newtonian framework. However, as noted in the introduction, white dwarfs are found to exist only below the Chandrasekar limit.…”

“…Since the electron gas in white dwarfs is completely degenerate, we evaluate the pressure P , internal energy ε int , and mass-density ρ 0 at absolute zero from the grand partition fucntion. Thus we obtain [4] the modified equation of state…”

“…Since a modification in the dispersion relation leads to a modified equation of state (EoS), it is apparent that the stellar structure of white dwarfs governed by its electron degenerate gas undergoes a measurable change if the stiffness of the EoS changes sufficiently. In fact it has been shown [3,4] that white dwarfs with modified EoS can support masses much higher than the Chandrasekhar limit that become "super-stable" when the hydrostatic equilibrium is governed by Newtonian gravity.…”