Effect of Generalized Uncertainty Principle on Main-Sequence Stars and White Dwarfs

Mohamed Moussa

doi:10.1155/2015/343284

Abstract

This paper addresses the effect of generalized uncertainty principle, emerged from different approaches of quantum gravity within Planck scale, on thermodynamic properties of photon, nonrelativistic ideal gases, and degenerate fermions. A modification in pressure, particle number, and energy density are calculated. Astrophysical objects such as main-sequence stars and white dwarfs are examined and discussed as an application. A modification in Lane-Emden equation due to a change in a polytropic relation caused by the presence of quantum gravity is investigated. The applicable range of quantum gravity parameters is estimated. The bounds in the perturbed parameters are relatively large but they may be considered reasonable values in the astrophysical regime.

Highlights

Different approaches for the quantum gravity have been proposed in string theory and black hole physics to provide a set of predictions for a minimum measurable length and an essential modification of the Heisenberg uncertainty principle (GUP) [1,2,3,4,5,6,7,8,9,10,11] and a modification in the fundamental commutation relation [xi, pj]
It is clear that the quantum gravity effect becomes significant when mass of the white dwarf gets very close to the Chandrasekhar limit in high density stars
Various approaches to quantum gravity such as string theory, black hole physics, and doubly special relativity predict a considerable modification in Heisenberg uncertainty principle to be a generalized uncertainty principle

Summary

Introduction

Different approaches for the quantum gravity have been proposed in string theory and black hole physics to provide a set of predictions for a minimum measurable length and an essential modification of the Heisenberg uncertainty principle (GUP) [1,2,3,4,5,6,7,8,9,10,11] and a modification in the fundamental commutation relation [xi, pj]. They found that the increase in the star energy leads to monotonical blowup of Fermi pressure which resists the gravitational collapse We will use this form of GUP (1) to investigate the implications of the quantum gravity on statistical properties of quantum gases. After redefining the new phase space we will put the partition function in a form that is consistent with GUP and rewrite the thermodynamic properties for quantum gases, namely, photons, nonrelativistic ideal gases, and fermions in degenerate state. Using these results we will follow the proposal which was investigated in [20] in studying the stability of main-sequence stars and white dwarf. A simple method is used to study the effect of quantum gravity in a different stage of stellar evolution and a modified mass-radius relation for the white dwarf is calculated and boundaries in the quantum gravity perturbative terms will be determined

Statistical Mechanics and GUP

Applications to Astrophysical Objects

Discussion