Effect of minimal length uncertainty on the mass–radius relation of white dwarfs

Mathew, Arun; Nandy, Malay K.

doi:10.1016/j.aop.2018.04.008

Cited by 20 publications

(21 citation statements)

References 46 publications

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“…The ultra-relativistic curve does not yield the Chandrasekhar limit: while the curve R(M ) tends to the original line M = M Ch as M → M + Ch , it is no longer bounded above when M increases. This means that white dwarfs can in principle gets arbitrarily large (for any M , there exists a nonzero R that satisfies the equilibrium equation between degenerate pressure and gravity; this is true for non-relativistic case too), consistent with the previous results obtained in [19] using a more rigorous method (see also [20][21][22]). In Fig.…”

Section: Generalized Uncertainty Principle and White Dwarfssupporting

confidence: 87%

Generalized uncertainty principle and white dwarfs redux: How the cosmological constant protects the Chandrasekhar limit

Ong

Yao

2018

Phys. Rev. D

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It was previously argued that generalized uncertainty principle (GUP) with a positive parameter removes the Chandrasekhar limit. One way to restore the limit is by taking the GUP parameter to be negative. In this work we discuss an alternative method that achieves the same effect: by including a cosmological constant term in the GUP (known as "extended GUP" in the literature). We show that an arbitrarily small but nonzero cosmological constant can restore the Chandrasekhar limit. We also remark that if the extended GUP is correct, then the existence of white dwarfs gives an upper bound for the cosmological constant, which -while still large compared to observation -is approximately 86 orders of magnitude smaller than the natural scale. I. GENERALIZED UNCERTAINTY PRINCIPLE AND WHITE DWARFSThe generalized uncertainty principle (GUP) is a quantum gravity inspired correction to the Heisenberg's uncertainty principle, which reads (in the simplest form)where L p = 1.616229×10 −35 m denotes the Planck length, and α is the GUP parameter typically taken as an O(1) positive number in theoretical calculations, i.e. one expects that the GUP correction becomes important at the Planck scale. GUP is largely heuristically "derived" from Gedanken-experiments under a specific quantum gravity theory (such as string theory [1-4]), or general considerations of gravitational correction to quantum mechanics [5][6][7][8]. GUP is useful as a phenomenological approach to study quantum gravitational effects. From phenomenological point of view, the GUP parameter can be treated as a free parameter a priori, which can be constrained from experiments [9][10][11][12]; α as large as 10 34 is consistent with the Standard Model of particle physics up to 100 GeV [9], while a tunneling current measurement gives α 10 21 [13]. See also [14][15][16].It turns out that GUP has a rather drastic effect on white dwarfs. This is somewhat of a surprise, since we do not usually expect GUP correction to be important for scale much above the Planck scale. A standardthough hand-wavy -method to obtain the behavior of degenerative matter is to consider the uncertainty principle ∆x∆p ∼ , and then take ∆x ∼ n −1/3 , where n is the number density n = N/V = M/(m e V ) of the white dwarf (here modeled as a pure electron star), where N is the total number of electrons, whereas V, M are, respectively, the volume and the total mass of the star, and m e Electronic address: ycong@yzu.edu.cn the electron mass. Then, the total kinetic energy in the non-relativistic case iswhere R is the radius of the star. Equating this with the magnitude of the gravitational binding energy |E g | ∼ GM 2 /R, one obtains the radius as a function of the mass:Thus the more massive a white dwarf is, the smaller it becomes. A similar derivation using the relativistic kinetic energy, and assuming that the momentum dominates over the rest mass of the electrons, allows one to obtain the Chandrasekhar limit up to a constant overall factor (see [17] for details). That is, the ultra-relativistic curve i...

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Section: Generalized Uncertainty Principle and White Dwarfssupporting

confidence: 87%

Generalized uncertainty principle and white dwarfs redux: How the cosmological constant protects the Chandrasekhar limit

Ong

Yao

2018

Phys. Rev. D

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“…The behavior of P (ξ) is shown in Figure 1b. We see that momenta higher than ξ max , determined by the cutoff p max of the noncommutative dispersion relation (6), are forbidden and the curve does not go beyond this limit.…”

Section: A Modified Thermodynamic Behaviormentioning

confidence: 86%

Noncommutative dispersion relation and mass-radius relation of white dwarfs

Mathew¹,

Nandy²

2018

Res. Astron. Astrophys.

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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

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“…It has not only been shown that the existence of a lower bound Δx 0 has an impact on the HUP but also on quantum mechanics in general, and the properties of atoms and molecules and their interactions in particular [58][59][60][61][62][63][64][65][66][67][68]. Needless to say that it also plays a role in astronomy and high energy physics [63,69].…”

Section: Generalized Uncertainty Principlementioning

confidence: 99%

Conjecture of new inequalities for some selected thermophysical properties values

Hohm

2019

J. Phys. Commun.

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In 2005 it was rigorously shown with string theory methods that there is a lower bound for the ratio of the shear viscosity η and the volume density of entropy s=S/V given byHere we extend this result in a heuristic manner to other ratios of thermophysical properties. We conjectured that there are rigorous non-zero lower bounds for the Lorenz number L as well as other combinations of equilibrium and transport properties. We suggest that the lower bounds and the corresponding inequalities can be written in terms of the Planck units. We show that some of the proposed new inequalities set severe constraints on the behavior and properties of ordinary matter.

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Effect of minimal length uncertainty on the mass–radius relation of white dwarfs

Cited by 20 publications

References 46 publications

Generalized uncertainty principle and white dwarfs redux: How the cosmological constant protects the Chandrasekhar limit

Generalized uncertainty principle and white dwarfs redux: How the cosmological constant protects the Chandrasekhar limit

Noncommutative dispersion relation and mass-radius relation of white dwarfs

Conjecture of new inequalities for some selected thermophysical properties values

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