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

Moussa, Mohamed

doi:10.1155/2015/343284

Cited by 28 publications

(19 citation statements)

References 37 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%

“…While the aim of this work is mainly theoretical, let us comment on the observational implications. As mentioned by Moussa in [20], the current observation indicates that some white dwarfs have smaller radii than theoretical predictions [42][43][44]. If we only consider GUP correction, then this favors a negative GUP parameter α since positive α leads to larger white dwarf for a given mass, not smaller.…”

Section: Discussionsupporting

confidence: 49%

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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%

Section: Discussionsupporting

confidence: 49%

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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“…Actually, at this energy level, i.e. p f ∼ 5m e c, the effect of the minimal length is, in turn, negligible [24,25].…”

Section: Removing the Chandrasekhar Limitmentioning

confidence: 91%

Generalized uncertainty principle and the maximum mass of ideal white dwarfs

Rashidi

2016

Annals of Physics

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The effect of a generalized uncertainty principle on the structure of an ideal white dwarf star is investigated. The equation describing the equilibrium configuration of the star is a generalized form of the Lane-Emden equation. It is proved that the star always has a finite size. It is then argued that the maximum mass of such an ideal white dwarf tends to infinity, as opposed to the conventional case where it has a finite value.

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“…It is possible that various other factors -such as coulomb correction, angular momentum correction (compact stars tend to spin very fast), magnetic field (compact stars tend to have a large magnetic field) correction, and lattice energy -may come into play to prevent white dwarfs from growing too massive [25]. Nevertheless, it would be more convincing if one could resolve this problem entirely within the context of GUP physics.…”

Section: Figmentioning

confidence: 99%

“…(11), as can be seen from Eq. (25). The vertical line M = 1 can never be reached and serves as the relativistic Chandrasekhar mass.…”

Section: How a Negative Sign Removes Both Infinitiesmentioning

confidence: 99%

Generalized uncertainty principle, black holes, and white dwarfs: a tale of two infinities

Ong

2018

J. Cosmol. Astropart. Phys.

126

118

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It is often argued that quantum gravitational correction to the Heisenberg's uncertainty principle leads to, among other things, a black hole remnant with finite temperature. However, such a generalized uncertainty principle also seemingly removes the Chandrasekhar limit, i.e., it permits white dwarfs to be arbitrarily large, which is at odds with astrophysical observations. We show that this problem can be resolved if the parameter in the generalized uncertainty principle is negative. We also discuss the Planck scale physics of such a model.

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

Cited by 28 publications

References 37 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

Generalized uncertainty principle and the maximum mass of ideal white dwarfs

Generalized uncertainty principle, black holes, and white dwarfs: a tale of two infinities

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