Effect of GUP on the Kepler problem and a variable minimal length

Ahmadi, Fatemeh; Khodagholizadeh, Jafar

doi:10.1139/cjp-2013-0354

Cited by 10 publications

(11 citation statements)

References 22 publications

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“…In this case, eqn. (17) then becomes ǫ = ±κǫ, (18) where the plus sign corresponds to the rolling solution since the further the particle departs from the unstable equilibrium, the faster it moves away from the equilibrium. So the rolling solution is…”

Section: Rolling Solutions Of Particles Near Black Hole Horizonmentioning

confidence: 99%

Minimal length effects on chaotic motion of particles around black hole horizon

Tao

Wang

2018

J. Cosmol. Astropart. Phys.

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Recently, it was conjectured that the Lyapunov exponent of chaotic motion of a particle in a black hole is universally bounded from above by the surface gravity of the black hole. On the other hand, the minimal length appears in various theories of quantum gravity and leads to the deformed canonical position-momentum commutation relation. In this paper, we use the Hamilton-Jacobi method to study effects of the minimal length on the motion of a massive particle perturbed away from an unstable equilibrium near the black hole horizon. We find that the minimal length effects make the particle move faster away from the equilibrium, and hence the corresponding Lyapunov exponent is greater than that in the usual case with the absence of the minimal length. It therefore shows that if the minimal length effects are taken into account, the conjectured universal bound on the Lyapunov exponent could be violated.

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Section: Rolling Solutions Of Particles Near Black Hole Horizonmentioning

confidence: 99%

Minimal length effects on chaotic motion of particles around black hole horizon

Tao

Wang

2018

J. Cosmol. Astropart. Phys.

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“…In the classical limit → 0, the effects of the minimal length can be studied in the classical context. For example, the minimal length effects have been analyzed for the observational tests of general relativity [37][38][39][40][41][42][43][44], classical harmonic oscillator [45,46], equivalence principle [47], Newtonian potential [48], the Schroinger-Newton equation [49], the weak cosmic censorship conjecture [50] and motion of particles near a black hole horizon [51,52]. Moreover, the minimal length corrections to the Hawking temperature were also obtained using the Hamilton-Jacobi method in [53][54][55][56].…”

mentioning

confidence: 99%

Chaotic Motion around a Black Hole under Minimal Length Effects

Guo,

Liang,

et al. 2020

Preprint

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We use the Melnikov method to identify chaotic behavior in geodesic motion perturbed by the minimal length effects around a Schwarzschild black hole. Unlike the integrable unperturbed geodesic motion, our results show that the perturbed homoclinic orbit, which is a geodesic joining the unstable circular orbit to itself, becomes chaotic in the sense that Smale horseshoes chaotic structure is present in phase space.

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“…where β is called the GUP (generalized uncertainty principle) parameter, and a non-zero minimum (comparable to the Planck length) is obtained for ∆x as √ β. Bearing quantum mechanics in mind, it is obvious that replacing HUP with GUP affects everything such as classical systems and orbit problem [3][4][5][6][7], Schrödinger equation [1,[8][9][10], high energy physics [11][12][13] and optics [14]. In this regard, Eq.…”

Section: Introductionmentioning

confidence: 99%

Minimal length implications on the Hartree–Fock theory

Sabet¹,

Moradpour²,

Bahadoran³

et al. 2021

Phys. Scr.

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Hartree-Fock approximation suffers from two inabilities including i) the divergence of electron Fermi velocity , and ii) existence of bandwidth not confirmed experimentally. Here, we study the effects of minimal length on the ground state energy of the electron gas in the Hartree-Fock approximation. Our results indicate that considering some mathematical terms, similar to those of used for the minimal length correction to the Hamiltonian of system, can eliminate the weaknesses of Hartree-Fock approximation. These corrections, on the other hand, can be considered as relativistic corrections of electron in solids. Physically, it is obtained that electrons in metals can be employed to test the quantum gravity scenario, if the value of its parameter (β) lies within the range of 2 to 10, depending on the used metal. Indeed, the latter addresses an upper bound on β which is comparable with previous works meaning that these types of systems may be employed in testing quantum gravity scenarios. To overcome the infinite Fermi velocity in Hartree-Fock method, the screening potential is used based on the Lindhard theory. We also find that considering the generalized Heisenberg uncertainly leads to some additional oscillating terms in the Friedel oscillations.

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Effect of GUP on the Kepler problem and a variable minimal length

Cited by 10 publications

References 22 publications

Minimal length effects on chaotic motion of particles around black hole horizon

Minimal length effects on chaotic motion of particles around black hole horizon

Chaotic Motion around a Black Hole under Minimal Length Effects

Minimal length implications on the Hartree–Fock theory

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