Noncommutative dispersion relation and mass-radius relation of white dwarfs

TL;DR

This paper investigates how quantum gravity effects, modeled through noncommutative geometry, modify the equation of state of white dwarf stars, potentially allowing for masses exceeding the Chandrasekhar limit, with implications for stellar physics.

Contribution

It introduces a modified dispersion relation due to quantum gravity effects and explores its impact on the mass-radius relation of white dwarfs, including the possibility of super-Chandrasekhar masses.

Findings

White dwarfs can have masses exceeding the Chandrasekhar limit due to noncommutative effects.

Neutronization effects restore masses close to the Chandrasekhar limit.

Numerical estimates for various elemental compositions support the theoretical predictions.

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 $^4He$ and $^{12}C$, and $^{16}O$ white dwarfs.