Regularization of Kepler problem in <i>κ</i>-spacetime

Guha, Partha; Harikumar, E.; Zuhair, N. S.

doi:10.1063/1.4966552

Cited by 5 publications

(5 citation statements)

References 37 publications

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“…Also, one may get a dependence through a deformed m appearing in eqn. (68) (see [37][38][39]53] (25) and (27)). Note that the dependence ofr and r s on a is through the combination ak 0 .…”

Section: Discussionmentioning

confidence: 99%

“…Also, one may get a dependence through a deformed m appearing in eqn. (68) (see [37][38][39]53]). Here we focused on the effect of deformed Schwarzschild metric in κ-spacetime on Hawking radiation.…”

Section: Discussionmentioning

confidence: 99%

“…This mapping is used to obtain a commutative models equivalent to the given κ-deformed model [35,36]. This approach was used to analyze Kepler system in κ-deformed spacetime and it was found that the deformed problem retains all the symmetries as the commutative Kepler problem [37][38][39]. Using this approach, change in the dimension of κ-spacetime with probe scale was analyzed in [40][41][42].…”

Section: Introductionmentioning

confidence: 99%

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Hawking radiation in κ-spacetime

Harikumar

Zuhair

2017

Int. J. Mod. Phys. A

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In this paper, we analyze the Hawking radiation of a κ-deformed-Schwarzschild black hole and obtain the deformed Hawking temperature. For this, we first derive deformed metric for the κ-spacetime, which in the generic case, is not a symmetric tensor and also has a momentum dependence. We show that the Schwarzschild metric obtained in the κ-deformed spacetime has a dependence on energy. We use the fact that the deformed metric is conformally flat in the 1 + 1 dimensions to solve the κ-deformed Klein-Gordon equation in the background of the Schwarzschild metric. The method of Bogoliubov coefficients is then used to calculate the thermal spectrum of κ-deformed-Schwarzschild black hole and show that the Hawking temperature is modified by the noncommutativity of the κ-spacetime.

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“…Also, one may get a dependence through a deformed m appearing in eqn. (68) (see [37][38][39]53] (25) and (27)). Note that the dependence ofr and r s on a is through the combination ak 0 .…”

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Hawking radiation in κ-spacetime

Harikumar

Zuhair

2017

Int. J. Mod. Phys. A

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“…Recently Kepler problem has been studied on noncommutative κ -spacetime and corresponding Bohlin-Arnold duality [11]. In particular, regularization of the Kepler problem on κ -spacetime in several different ways [12]. Regularization is a mathematical procedure to cure this singularity.…”

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confidence: 99%

Jacobi–Maupertuis metric and Kepler equation

Chanda

Gibbons

Guha

2017

Int. J. Geom. Methods Mod. Phys.

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This article studies the application of the Jacobi-Eisenhart lift, Jacobi metric and Maupertius transformation to the Kepler system. We start by reviewing fundamentals and the Jacobi metric. Then we study various ways to apply the lift to Kepler related systems: first as conformal description and Bohlin transformation of Hooke's oscillator, second in contact geometry, third in Houri's transformation [13], coupled with Milnor's construction [21] with eccentric anomaly.MSC classes: 70H06, 53D25, 53B20, 70F16.

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“…In [27][28][29], we have studied the regularization of central potentials in non-commutative space-time. Thus it is of interest to see whether the results obtained here can be generalized to non-commutative space-time.…”

Section: Discussionmentioning

confidence: 99%

Regularization of central forces with damping in two and three dimensions

2021

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Two damped, central force systems are investigated and equivalent, undamped systems are obtained. The dynamics of a particle moving in 1 r potential and subjected to a damping force is shown to be regularized a la Levi-Civita. This mapping is then elevated to the corresponding quantum mechanical systems and using it, the energy spectrum of the former is calculated. Mapping of a particle moving in a harmonic potential subjected to damping to an undamped system is then derived using Bohlin-Sudman transformation, for both classical and quantum regime.

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Regularization of Kepler problem in κ-spacetime

Cited by 5 publications

References 37 publications

Hawking radiation in κ-spacetime

Hawking radiation in κ-spacetime

Jacobi–Maupertuis metric and Kepler equation

Regularization of central forces with damping in two and three dimensions

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