Natural Science, 2015, 7, 210-225 Published Online April 2015 in SciRes. How to cite this paper: El Naschie, M.S. (2015) Kerr Black Hole Geometry Leading to Dark Matter and Dark Energy via E-Infinity Theory and the Possibility of a Nano Spacetime Singularities Reactor. Natural Science, 7, 210-225. Kerr Black Hole Geometry Leading to Dark Matter and Dark Energy via E-Infinity Theory and the Possibility of a Nano Spacetime Singularities Reactor* Mohamed S. El Naschie Department of Physics, University of Alexandria, Alexandria, Egypt Email: [email protected]Received 18 March 2015; accepted 21 April 2015; published 23 April 2015 Copyright © 2015 by author and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). Abstract The present paper is basically a synthesis resulting from incorporating Kerr spinning black hole geometry into E-infinity topology, then letting the result bares on the vacuum zero point Casimir effect as well as the cosmic dark energy and dark matter density. In E-infinity theory a quantum particle is represented by a Hausdorff dimension φwhere ()251φ=. The quantum wave on the other hand is represented by 2φ. To be wave and a particle simultaneously intersection the-ory leads us to ()()23φφφ=which will be shown here to be twice the value of the famous Casimir force of the vacuum for a massless scalar field. Thus in the present work a basically topological in-terpretation of the Casimir effect is given as a natural intrinsic property of the geometrical topo-logical structure of the quantum-Cantorian micro spacetime. This new interpretation compliments the earlier conventional interpretation as vacuum fluctuation or as a Schwinger source and links the Casimir energy to the so called missing dark energy density of the cosmos. From the view point of the present work Casimir pressure is a local effect acting on the Casimir plates constituting the local boundary condition while dark energy is nothing but the global combined effect of infinitely many quantum waves acting on the Möbius-like boundary of the holographic boundary of the en-tire universe. Since this higher dimensional Möbius-like boundary is one sided, there is no outside to balance the internal collective Casimir pressure which then manifests itself as the force behind cosmic expansion, that is to say, dark energy. Thus analogous to the exact irrational value of ordi-nary energy density of spacetime ()()522φ=E Omcwe now have ()()()32Casimir2φ=Pcdwhere cis the speed of light, mis the mass, is the Planck constant and dis the plate sepa-*Dedicated to all those who genuinely believe in the science and reality of zero point spacetime vacuum energy.

M. S. El. Naschie 211 ration. In addition the new emerging geometry combined with the topology of E-infinity theory

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