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

arXiv comment4 figures

References in corpus (24)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• Hilbert Space Representation of the Minimal Length Uncertainty Relation
• Relativity in space-times with short-distance structure governed by an observer-independent (Planckian) length scale
• A Generalized Uncertainty Principle in Quantum Gravity
• The type Ia supernova SNLS-03D3bb from a super-Chandrasekhar-mass white dwarf star
• Nearby Supernova Factory Observations of SN 2007if: First Total Mass Measurement of a Super-Chandrasekhar-Mass Progenitor
• White Dwarf Mass Distribution in the SDSS
• Limits to Quantum Gravity Effects from Observations of TeV Flares in Active Galaxies
• The Luminous and Carbon-Rich Supernova 2006gz: A Double Degenerate Merger?
• Fourteen Months of Observations of the Possible Super-Chandrasekhar Mass Type Ia Supernova 2009dc
• A Higher Order GUP with Minimal Length Uncertainty and Maximal Momentum
• Early phase observations of extremely luminous Type Ia Supernova 2009dc
• The Lowest Mass White Dwarf
• Strongly magnetized cold electron degenerate gas: Mass-radius relation of the magnetized white dwarf
• The relativistic Feynman-Metropolis-Teller theory for white-dwarfs in general relativity
• On the progenitors of super-Chandrasekhar mass type Ia supernovae
• Probing a Possible Vacuum Refractive Index with Gamma-Ray Telescopes
• Towards a Noncommutative Astrophysics
• Generalized Uncertainty Principle Removes The Chandrasekhar Limit
• White dwarfs as test objects of Lorentz violations
• On Modified Dispersion Relations and the Chandrasekhar Mass Limit
• Effect of minimal length uncertainty on the mass-radius relation of white dwarfs
• Merging White Dwarfs and Thermonuclear Supernovae

Cited by in corpus (1)

• Prospect of Chandrasekhar's limit against modified dispersion relation