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On the quasi-normal modes of a Schwarzschild white hole for the lower angular momentum and perturbation by non-local fractional operators

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  • Kubeka, Amos S.
  • Doungmo Goufo, Emile F.
  • Khumalo, Melusi

Abstract

We investigate conditions for the quasi-normal modes of a Schwarzschild white hole for lower angular momentum. In determining these normal modes, we use numerical methods to solve the solution of the linearized Einstein vacuum equations in null cone coordinates. The same model is generalized to non-local fractional operator theory where the model is solved numerically thanks to a method proposed by Toufik and Atangana. In fact, approaching this kind of problem analytically seems to be an impossible task as comprehensively articulated in the literature. We show existence of quasi-normal modes of a Schwarzschild white hole for lower angular momentum l=2. Moreover, the non-local fractional operator appears to be a perturbator factor for the system as shown by numerical simulations that compare the types of dynamics in the system.

Suggested Citation

  • Kubeka, Amos S. & Doungmo Goufo, Emile F. & Khumalo, Melusi, 2018. "On the quasi-normal modes of a Schwarzschild white hole for the lower angular momentum and perturbation by non-local fractional operators," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 348-357.
    • Handle: RePEc:eee:chsofr:v:116:y:2018:i:c:p:348-357
    DOI: 10.1016/j.chaos.2018.09.047
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    References listed on IDEAS

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    1. Atangana, Abdon, 2018. "Non validity of index law in fractional calculus: A fractional differential operator with Markovian and non-Markovian properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 688-706.
    2. Atangana, Abdon & Gómez-Aguilar, J.F., 2018. "Fractional derivatives with no-index law property: Application to chaos and statistics," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 516-535.
    3. Saad, Khaled M. & Gómez-Aguilar, J.F., 2018. "Analysis of reaction–diffusion system via a new fractional derivative with non-singular kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 703-716.
    4. Atangana, Abdon & Gómez-Aguilar, J.F., 2017. "Hyperchaotic behaviour obtained via a nonlocal operator with exponential decay and Mittag-Leffler laws," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 285-294.
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