Author(s)

Mohamed S. El Naschie

Department of Physics, University of Alexandria, Alexandria, Egypt.

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 Φ where Φ =2/(√5+1) . The quantum wave on the other hand is represented by Φ² . To be wave and a particle simultaneously intersection theory leads us to (Φ) (Φ)²= Φ³ 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 interpretation of the Casimir effect is given as a natural intrinsic property of the geometrical topological 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 M?bius-like boundary of the holographic boundary of the entire universe. Since this higher dimensional M?bius-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 ordinary energy density of spacetime E(O)=(Φ⁵/2) mc² we now have P (Casimir) = (Φ³/2)(ch/d²) where c is the speed of light, m is the mass, h is the Planck constant and d is the plate separation. In addition the new emerging geometry combined with the topology of E-infinity theory leads directly to identifying dark matter with the quasi matter of the ergosphere. As a direct consequence of this new insight E=mc² which can be written as E = E (O) + E (D) where the exact rational approximation is E (O)=mc²/22 is the ordinary energy density of the cosmos and the exact rational approximation E (D)=mc²/(21/22) is the corresponding dark energy which could be subdivided once more albeit truly approximately into E(D)=mc²/(5/22) +mc²/(16/22)  where 5 is the Kaluza Klein spacetime dimension, 16 are the bosonic extra dimensions of Heterotic superstrings and 5/22 □ 22% is approximately the density of the dark matter-like energy of the ergosphere of the Kerr geometry. As for the actual design of our nano reactor, this is closely related to branching clusters of polymer, frequently called lattice animals. In other words we will have Casimir spheres instead of Casimir plates and these spheres will be basically nano particles modelling lattice animals. Here D= 4 will be regarded as spacetime dimensionality while D=6 of percolations are the compactified super string dimensions and D=8 is the dimension of a corresponding super space.

Casimir Effect, Dark Energy, E-Infinity, Cantorian Spacetime, Kerr Spacetime Geometry, Energy from the Ergosphere, Spinning Black Holes, Nano Spacetime Reactors, Kaluza-Klein Spacetime, Heterotic Superstrings

El Naschie, M. (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. doi: 10.4236/ns.2015.74024.