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Hypersingular integral equations, Kähler manifolds and Thurston mirroring effect in ϵ(∞) Cantorian spacetime

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  • Iovane, G.

Abstract

In this work starting from some earlier results on hypersingular integral equations and analyzing a more realistic model of gravitational waveguides on a Cantorian spacetime we obtain a description of our Universe according to Kähler manifold in the context of El Naschie’s ϵ(∞) Cantorian space-time. In particular, we consider filamentary and planar large scale structures as possible refraction channels for electromagnetic radiation coming from cosmological structures. From this vision the Universe appears like a large self-similar adaptive mirrors set. This is made evident through numerical simulations. Consequently, an infinite Universe is just an optical illusion that is produced by mirroring effects connected to the large scale structure of a finite and not so large Universe.

Suggested Citation

  • Iovane, G., 2007. "Hypersingular integral equations, Kähler manifolds and Thurston mirroring effect in ϵ(∞) Cantorian spacetime," Chaos, Solitons & Fractals, Elsevier, vol. 31(5), pages 1041-1053.
    • Handle: RePEc:eee:chsofr:v:31:y:2007:i:5:p:1041-1053
    DOI: 10.1016/j.chaos.2006.03.109
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    References listed on IDEAS

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    1. El Naschie, M.S., 2006. "Hilbert, Fock and Cantorian spaces in the quantum two-slit gedanken experiment," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 39-42.
    2. Iovane, G., 2006. "Cantorian spacetime and Hilbert space: Part I—Foundations," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 857-878.
    3. Mackay, Alan L., 1982. "Crystallography and the penrose pattern," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 114(1), pages 609-613.
    4. El Naschie, M.S., 2005. "Non-Euclidean spacetime structure and the two-slit experiment," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 1-6.
    5. Iovane, G. & Giordano, P., 2005. "Hypersingular integral equations, waveguiding effects in Cantorian Universe and genesis of large scale structures," Chaos, Solitons & Fractals, Elsevier, vol. 25(4), pages 879-896.
    6. El Naschie, M.S., 2006. "Hilbert space, the number of Higgs particles and the quantum two-slit experiment," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 9-13.
    7. George F. R. Ellis, 2003. "The shape of the Universe," Nature, Nature, vol. 425(6958), pages 566-567, October.
    8. Iovane, G. & Gargiulo, G. & Zappale, E., 2006. "A Cantorian potential theory for describing dynamical systems on El Naschie’s space–time," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 588-598.
    9. Iovane, G., 2006. "Cantorian space–time, Fantappie’s final group, accelerated universe and other consequences," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 618-629.
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    Cited by:

    1. Halayka, S., 2009. "Is the anisotropic interaction of luminous matter responsible for the extrinsic gravitation usually attributed to exotic dark matter?," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 113-118.

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