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Hypersingular integral equations, waveguiding effects in Cantorian Universe and genesis of large scale structures

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  • Iovane, G.
  • Giordano, P.

Abstract

In this work we introduce the hypersingular integral equations and analyze a realistic model of gravitational waveguides on a cantorian space-time. A waveguiding effect is considered with respect to the large scale structure of the Universe, where the structure formation appears as if it were a classically self-similar random process at all astrophysical scales. The result is that it seems we live in an El Naschie’s ϵ(∞) Cantorian space-time, where gravitational lensing and waveguiding effects can explain the appearing Universe. 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, thanks to three numerical simulations. Consequently, an infinite Universe is just an optical illusion that is produced by mirroring effects connected with the large scale structure of a finite and not a large Universe.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:25:y:2005:i:4:p:879-896
    DOI: 10.1016/j.chaos.2004.11.045
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    1. Mackay, Alan L., 1982. "Crystallography and the penrose pattern," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 114(1), pages 609-613.
    2. El Naschie, M.S., 2005. "On 336 kissing spheres in 10 dimensions, 528 P-Brane states in 11 dimensions and the 60 elementary particles of the standard model," Chaos, Solitons & Fractals, Elsevier, vol. 24(2), pages 447-457.
    3. George F. R. Ellis, 2003. "The shape of the Universe," Nature, Nature, vol. 425(6958), pages 566-567, October.
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    1. Iovane, Gerardo & Giordano, Paola, 2007. "Wavelets and multiresolution analysis: Nature of ε(∞) Cantorian space–time," Chaos, Solitons & Fractals, Elsevier, vol. 32(3), pages 896-910.
    2. 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.
    3. Iovane, G., 2006. "Cantorian spacetime and Hilbert space: Part I—Foundations," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 857-878.
    4. Iovane, G., 2006. "Cantorian space–time and Hilbert space: Part II—Relevant consequences," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 1-22.

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