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Fractal structures in the deflection of light by a pair of charged black holes

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  • de Souza Filho, Edson E.
  • Mathias, Amanda C.
  • Viana, Ricardo L.

Abstract

The deflection of light by a pair of black holes can be considered an open conservative non-linear dynamic system. The basis of our approach is our understanding of strong gravitational lensing and the geodesic movement of light. We obtain a two-dimensional map that sets out the impact parameter and the escape angle when the light gets deflected by each black hole. Being a non-integrable system, the chaotic area-filling orbits occur in a specific parameter range. Fractal structures are related to the existence of a non-attractive invariant chaotic set. This can be seen in the dynamics of these chaotic orbits. The light-ray that enters the system has two potential defined outcomes. Either the light ray can diverge to infinity or it will fall into one of the two black holes. We describe the escape basins and their boundaries, adopting two methods: firstly the corresponding basin and basin boundary entropies and secondly the computation of the uncertainty exponents.

Suggested Citation

  • de Souza Filho, Edson E. & Mathias, Amanda C. & Viana, Ricardo L., 2021. "Fractal structures in the deflection of light by a pair of charged black holes," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    • Handle: RePEc:eee:chsofr:v:150:y:2021:i:c:s0960077921004938
    DOI: 10.1016/j.chaos.2021.111139
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    References listed on IDEAS

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    1. Mathias, A.C. & Kroetz, T. & Caldas, I.L. & Viana, R.L., 2017. "Chaotic magnetic field lines and fractal structures in a tokamak with magnetic limiter," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 588-598.
    2. Hansen, Matheus & da Costa, Diogo Ricardo & Caldas, Iberê L. & Leonel, Edson D., 2018. "Statistical properties for an open oval billiard: An investigation of the escaping basins," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 355-362.
    3. Mathias, A.C. & Viana, R.L. & Kroetz, T. & Caldas, I.L., 2017. "Fractal structures in the chaotic motion of charged particles in a magnetized plasma under the influence of drift waves," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 681-694.
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