NS  Vol.7 No.4 , April 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
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&#246bius-like boundary of the holographic boundary of the entire universe. Since this higher dimensional M&#246bius-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.

Cite this paper
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.
[1]   El Naschie, M.S. (2015) Three Quantum Particles Hardy Entanglement from the Topology of Cantorian-Fractal Spacetime and the Casimir Effect as Dark Energy—A Great Opportunity for Nanotechnology. American Journal of Nano Research and Applications, 3, 1-5.

[2]   El Naschie, M.S. (2014) Casimir-Like Energy as a Double Eigenvalue of Quantumly Entangled System Leading to the Missing Dark Energy Density of the Cosmos. International Journal of High Energy Physics, 1, 55-63.

[3]   El Naschie, M.S. (2014) The Measure Concentration of Convex Geometry in a Quasi Banach Spacetime behind the Supposedly Missing Dark Energy of the Cosmos. American Journal of Astronomy & Astrophysics, 2, 72-77.

[4]   Slezak, M. (2015) Quantum Wave Function Gets Real. New Scientist, 225, 14. http://dx.doi.org/10.1016/S0262-4079(15)60242-1

[5]   El Naschie, M.S. (2015) Dark Energy and Its Cosmic Density from Einstein’s Relativity and Gauge Fields Renormalization Leading to the Possibility of a New ‘tHooft Quasi Particle. The Open Astronomy Journal, 8, 1-17. http://dx.doi.org/10.2174/1874381101508010001

[6]   El Naschie, M.S. (2015) Banach Spacetime-Like Dvoretzky Volume Concentration as Cosmic Holographic Dark Energy. International Journal of High Energy Physics, 2, 13-21.

[7]   El Naschie, M.S. (2014) From E = mc2 to E = mc2/22—A Short Account of the Most Famous Equation in Physics and Its Hidden Quantum Entanglement Origin. Journal of Quantum Information Science, 4, 284-291. http://dx.doi.org/10.4236/jqis.2014.44023

[8]   El Naschie, M.S. (2014) The Hidden Quantum Entanglement Roots of E = mc2 and Its Genesis to E = mc2/22 Plus mc2(21/22) Confirming Einstein’s Mass-Energy Formula. American Journal of Electromagnetics and Applications, 2, 39-44. http://dx.doi.org/10.11648/j.ajea.20140205.11

[9]   El Naschie, M.S. (1999) From Implosion to Fractal Spheres. A Brief Account of the Historical Development of Scientific Ideas Leading to the Trinity Test and Beyond. Chaos, Solitons & Fractals, 10, 1955-1965. http://dx.doi.org/10.1016/S0960-0779(99)00030-2

[10]   El Naschie, M.S. and Al Athel, S. (2000) Estimating the Eigenvalue of Fast Reactors and Cantorian Space. Chaos, Solitons & Fractals, 11, 1957-1961. http://dx.doi.org/10.1016/S0960-0779(99)00069-7

[11]   El Naschie, M.S. (2000) On Nishina’s Estimate of the Critical Mass for Fussion and Early Nuclear Research in Japan. Chaos, Solitons & Fractals, 11, 1809-1818. http://dx.doi.org/10.1016/S0960-0779(99)00172-1

[12]   El Naschie, M.S. (2000) Remarks on Heisenberg’s Farm-Hall Lecture on the Critical Mass of Fast Neutron Fission. Chaos, Solitons & Fractals, 11, 1327-1333. http://dx.doi.org/10.1016/S0960-0779(99)00136-8

[13]   El Naschie, M.S. and Hussein, A. (2000) On the Eigenvalue of Nuclear Reaction and Self-Weight Buckling. Chaos, Solitons & Fractals, 11, 815-818. http://dx.doi.org/10.1016/S0960-0779(99)00106-X

[14]   El Naschie, M.S. (2000) Elastic Buckling Loads and Fission Critical Mass as an Eigenvalue of a Symmetry Breaking Bifurcation. Chaos, Solitons & Fractals, 11, 631-639. http://dx.doi.org/10.1016/S0960-0779(99)00063-6

[15]   El Naschie, M.S. (2000) On the Zel’dovich-Khuriton Critical Mass for Fast Fission. Chaos, Solitons & Fractals, 11, 819-824. http://dx.doi.org/10.1016/S0960-0779(99)00113-7

[16]   El Naschie, M.S. (2000) On the Eigenvalue of Transport Reaction Involving Fast Neutrons. Chaos, Solitons & Fractals, 11, 929-934. http://dx.doi.org/10.1016/S0960-0779(99)00066-1

[17]   El Naschie, M.S. (2000) Heisenberg’s Critical Mass Calculations for an Explosive Nuclear Reaction. Chaos, Solitons & Fractals, 11, 987-997. http://dx.doi.org/10.1016/S0960-0779(99)00110-1

[18]   El Naschie, M.S. (1998) Chaos and Fractals in Nano and Quantum Technology. Chaos, Solitons & Fractals, 9, 1793- 1802.

[19]   El Naschie, M.S. (2006) Nanotechnology for the Developing World. Chaos, Solitons & Fractals, 30, 769-773. http://dx.doi.org/10.1016/j.chaos.2006.04.037

[20]   El Naschie, M.S. (2007) The Political Economy of Nanotechnology and the Developing World. International Journal of Electrospun Nanofibrers and Applications, 1, 41-50.

[21]   El Naschie, M.S. (1998) Some Tentative Proposals for the Experimental Verification of Cantorian Micro Spacetime. Chaos, Solitons & Fractals, 9, 143-144. http://dx.doi.org/10.1016/S0960-0779(97)00175-6

[22]   Johnston, H. (2012) Physicists Solve Casimir Conundrum. Physicsworld.com. 18 July 2012.

[23]   Rencroft, S. and Swain, J. (1998) What Is the Casimir Effect? Scientific American, 22 June 1998.

[24]   Wongjun, P. (2015) Casimir Dark Energy, Stabilization of the Extra Dimensions and Gauss-Bonnet Term. The European Physical Journal C, 75, 6. http://dx.doi.org/10.1140/epjc/s10052-014-3237-0

[25]   El Naschie, M.S. (2007) A Review of Applications and Results of E-Infinity Theory. International Journal of Nonlinear Sciences and Numerical Simulation, 8, 11-20. http://dx.doi.org/10.1515/IJNSNS.2007.8.1.11

[26]   Smolin, L. (2001) The Strong and the Weak Holographic Principles. Nuclear Physics B, 601, 209-247. http://dx.doi.org/10.1016/S0550-3213(01)00049-9

[27]   El Naschie, M.S. (2006) Holographic Dimensional Reduction: Center Manifold Theorem and E-Infinity. Chaos, Solitons & Fractals, 29, 816-822. http://dx.doi.org/10.1016/j.chaos.2006.01.013

[28]   Misner, C., Thorne, K. and Wheeler, J.A. (1973) Gravitation. Freeman, New York.

[29]   El Naschie, M.S. (2003) Kleinian Groups in E-Infinity and Their Connection to Particle Physics and Cosmology. Chaos, Solitons & Fractals, 16, 637-649. http://dx.doi.org/10.1016/S0960-0779(02)00489-7

[30]   El Naschie, M.S. (2005) A Guide to the Mathematics of E-Infinity Cantorian Spacetime Theory. Chaos, Solitons & Fractals, 25, 955-964.

[31]   El Naschie, M.S. (2004) The Concepts of E-Infinity: An Elementary Introduction to the Cantorian-Fractal Theory of Quantum Physics. Chaos, Solitons & Fractals, 22, 495-511. http://dx.doi.org/10.1016/j.chaos.2004.02.028

[32]   El Naschie, M.S. (2003) Complex Vacuum Fluctuation as a Chaotic “Limit” Set of Any Kleinian Group Transformation and the Mass Spectrum of High Energy Particle Physics via Spontaneous Self Organization. Chaos, Solitons & Fractals, 17, 631-638. http://dx.doi.org/10.1016/S0960-0779(02)00630-6

[33]   El Naschie, M.S. (2003) Modular Groups in Cantorian E-Infinity High Energy Physics. Chaos, Solitons & Fractals, 16, 353-366. http://dx.doi.org/10.1016/S0960-0779(02)00440-X

[34]   El Naschie, M.S. (1994) On Certain “Empty” Cantor Sets and Their Dimensions. Chaos, Solitons & Fractals, 4, 293- 296. http://dx.doi.org/10.1016/0960-0779(94)90152-X

[35]   He, J.H., Xu, L., Zhang, L.N. and Wu, X.H. (2007) Twenty-Six Dimensional Polytope and High Energy Spacetime Physics. Chaos, Solitons & Fractals, 33, 5-13. http://dx.doi.org/10.1016/j.chaos.2006.10.048

[36]   El Naschie, M.S. (1994) Is Quantum Space a Random Cantor Set with a Golden Mean Dimension at the Core? Chaos, Solitons & Fractals, 4, 177-179. http://dx.doi.org/10.1016/0960-0779(94)90141-4

[37]   El Naschie, M.S. (2008) Mathematical Foundation of E-Infinity via Coxeter and Reflection Groups. Chaos, Solitons & Fractals, 37, 1267-1268. http://dx.doi.org/10.1016/j.chaos.2008.02.001

[38]   El Naschie, M.S. (1995) Banach-Tarski Theorem and Cantorian Micro Spacetime. Chaos, Solitons & Fractals, 5, 1503-1508. http://dx.doi.org/10.1016/0960-0779(95)00052-6

[39]   El Naschie, M.S. (1995) On the Initial Singularity and the Banach-Tarski Theorem. Chaos, Solitons & Fractals, 5, 1391-1392. http://dx.doi.org/10.1016/0960-0779(95)99645-2

[40]   El Naschie, M.S. (1998) Cobe Satellite Measurement, Hyperspheres, Superstrings and the Dimension of Spacetime. Chaos, Solitons & Fractals, 9, 1445-1471. http://dx.doi.org/10.1016/S0960-0779(98)00120-9

[41]   El Naschie, M.S. (2001) Infinite Dimensional Branes and the E-Infinity Topology of Heterotic Superstrings. Chaos, Solitons & Fractals, 12, 1047-1055. http://dx.doi.org/10.1016/S0960-0779(00)00130-2

[42]   El Naschie, M.S. (2007) Ji-Huan He’s Ten Dimensional Polytope and High Energy Particle Physics. International Journal of Nonlinear Sciences & Numerical Simulation, 8, 475-476. http://dx.doi.org/10.1515/IJNSNS.2007.8.4.475

[43]   El Naschie, M.S. (1999) Hyperdimensional Geometry and the Nature of Physical Spacetime. Chaos, Solitons & Fractals, 10, 155-158. http://dx.doi.org/10.1016/S0960-0779(98)00235-5

[44]   Finkelstein, D. (1982) Quantum Sets and Clifford Algebras. International Journal of Theoretical Physics, 21, 489-503. http://dx.doi.org/10.1007/BF02650180

[45]   El Naschie, M.S. (2002) Derivation of the Threshold and Absolute Temperature Tc = 273.16 K from the Topology of Quantum Spacetime. Chaos, Solitons & Fractals, 14, 1117-1120. http://dx.doi.org/10.1016/S0960-0779(02)00053-X

[46]   El Naschie, M.S. (2008) Quarks Confinement via Kaluza-Klein Theory as a Topological Property of Quantum Classical Spacetime Phase Transition. Chaos, Solitons & Fractals, 35, 825-829. http://dx.doi.org/10.1016/j.chaos.2007.08.057

[47]   El Naschie, M.S. (2002) On a Class of General Theories for High Energy Particle Physics. Chaos, Solitons & Fractals, 14, 649-668. http://dx.doi.org/10.1016/S0960-0779(02)00033-4

[48]   He, J.H. (2009) Hilbert Cube Model for Fractal Spacetime. Chaos, Solitons & Fractals, 42, 2754-2759. http://dx.doi.org/10.1016/j.chaos.2009.03.182

[49]   Lomas, R. (1999) The Man Who Invented the Twentieth Century: Nicola Tesla, Forgotten Genius of Electricity. Headline Books, London.

[50]   Helal, M., Marek-Crnjac, L. and He, J.H. (2013) The Three Page Guide to the Most Important Results of M. S. El Naschie’s Research in E-Infinity Quantum Physics and Cosmology. Open Journal of Microphysics, 3, 141-145. http://dx.doi.org/10.4236/ojm.2013.34020

[51]   El Naschie, M.S. (2004) A Review of E-Infinity Theory and the Mass Spectrum of High Energy Particle Physics. Chaos, Solitons & Fractals, 19, 209-236. http://dx.doi.org/10.1016/S0960-0779(03)00278-9

[52]   El Naschie, M.S. (2009) The Theory of Cantorian Spacetime and High Energy Particle Physics (An Informal Review). Chaos, Solitons & Fractals, 41, 2635-2646. http://dx.doi.org/10.1016/j.chaos.2008.09.059

[53]   Marek-Crnjac, L. and He, J.H. (2013) An Invitation to El Naschie’s Theory of Cantorian Space-Time and Dark Energy. International Journal of Astronomy and Astrophysics, 3, 464-471. http://dx.doi.org/10.4236/ijaa.2013.34053

[54]   El Naschie, M.S. (2013) A Resolution of Cosmic Dark Energy via a Quantum Entanglement Relativity Theory. Journal of Quantum Information Science, 3, 23-26. http://dx.doi.org/10.4236/jqis.2013.31006

[55]   El Naschie, M.S. (2013) What Is the Missing Dark Energy in a Nutshell and the Hawking-Hartle Quantum Wave Collapse. International Journal of Astronomy & Astrophysics, 3, 205-211. http://dx.doi.org/10.4236/ijaa.2013.33024

[56]   El Naschie, M.S. (2013) Topological-Geometrical and Physical Interpretation of the Dark Energy of the Cosmos as a “Halo” Energy of the Schrodinger Quantum Wave. Journal of Modern Physics, 4, 591-596. http://dx.doi.org/10.4236/jmp.2013.45084

[57]   Peat, F.D. (1983) In Search of Nikola Tesla. Ashgrove Publications, London & Bath.

[58]   Susskind, L. and Lindesay, J. (2005) The Holographic Universe. World Scientific, Singapore.

[59]   Stiglitz, J. and Bilmes, L. (2008) The Three Trillion Dollar War: The True Cost of The Iraq Conflict. Allen-Lane, Penguin Books, London.

[60]   El Naschie, M.S. (2013) A Unified Newtonian-Relativistic Quantum Resolution of Supposedly Missing Dark Energy of the Cosmos and the Constancy of the Speed of Light. International Journal of Modern Nonlinear Theory & Application, 2, 43-54. http://dx.doi.org/10.4236/ijmnta.2013.21005

[61]   Malek, C. (2015) Abu Dhabi Crown Prince Details UAE Leaders’ Vision of Future without Oil. The National Newspaper, UAE, 10th February 2015. http://www.thenational.ae/uae/government/abu-dhabi-crown-prince-details-uae-leaders-vision-of-future-without-oil?utm_content='%20vision%20of%20future%20without%20oil

[62]   Zee, A. (2003) Quantum Field Theory in a Nutshell. Princeton University Press, Princeton.

[63]   Duplantier, B. and Rivasseau, V., Eds. (2003) Vacuum Energy-Renormalization. Birkhauser, Basel.

[64]   Milonni, P.W. (1994) The Quantum Vacuum. Academic Press, Boston.

[65]   Parsegian, V.A. (2006) van der Waals Forces. Cambridge University Press, Cambridge.

[66]   Huang, K. (2007) Fundamental Forces of Nature. World Scientific, Singapore. http://dx.doi.org/10.1142/6447

[67]   Wapner, L.M. (2005) The Pea and the Sun. A.K. Peters Ltd., Wellesley.

[68]   Auffray, J.P. (2015) E-Infinity, Zero Set, Absolute Space and the Photon Spin. Journal of Modern Physics, 6, 536-545. http://dx.doi.org/10.4236/jmp.2015.65058

[69]   Connes, A. (1994) Noncommutative Geometry. Academic Press, San Diego. (See in particular pages 88-93 and Fig. II.4)

[70]   Wald, R.M. (1984) General Relativity. The University of Chicago Press, Chicago and London. (See in particular page 319 and Fig. 12.6)

[71]   Sternberg, S. (2012) Curvature in Mathematics and Physics. Dover Publications, New York.

[72]   El Naschie, M.S. (2011) On Twistors in Cantorian E-Infinity Space. Chaos, Solitons & Fractals, 12, 741-746. http://dx.doi.org/10.1016/S0960-0779(00)00193-4

[73]   El Naschie, M.S. (2015) On a Casimir-Dark Energy Nano Reactor. American Journal of Nano Research and Application, 3, 12-16.

[74]   Ho, M.W., El Naschie, M. and Vitiello, G. (2015) Is Spacetime Fractal and Quantum Coherent in the Golden Mean. Global Journal of Science Frontier Research—A: Physics and Space Science, 15, 61-80.

[75]   El Naschie, M.S. (2015) From Kantian-Reinen Vernunft to the Real Dark Energy Density of the Cosmos via the Measure Concentration of Convex Geometry in Quasi Banach Spacetime. Open Journal of Philosophy, 5, 123-130. http://dx.doi.org/10.4236/ojpp.2015.51014

[76]   El Naschie, M.S. (2015) Dark Energy and Its Cosmic Density from Einstein’s Relativity and Gauge Field Renormalization Leading to the Possibility of a New ‘tHooft Quasi Particle. The Open Astronomy Journal, 8, 1-17. http://dx.doi.org/10.2174/1874381101508010001

[77]   Stauffer, D. and Stanley, H.E. (1996) From Newton to Mandelbrot. 2nd Edition, Springer, Berlin.

[78]   El Naschie, M.S. (1998) Branching Polymers and the Fractal Cantorian Spacetime. Chaos, Solitons & Fractals, 9, 135-141. http://dx.doi.org/10.1016/S0960-0779(97)00133-1

[79]   El Naschie, M.S. (1997) The Bethe Lattice and the Dimension of Micro Spacetime. Chaos, Solitons & Fractals, 8, 1887-1889. http://dx.doi.org/10.1016/S0960-0779(97)00130-6

[80]   Miltao, M.S.R. (2008) Casimir Energy for a Double Spherical Shell: A Global Mode Sum Approach. Physical Review D, 78, Article ID: 065023. http://dx.doi.org/10.1103/PhysRevD.78.065023

[81]   El Naschie, M.S. (2015) Computing Dark Energy and Ordinary Energy of the Cosmos as a Double Eigenvalue Problem. Journal of Modern Physics, 6, 348-395. http://dx.doi.org/10.4236/jmp.2015.64042

[82]   El Naschie, M.S. (2015) A Fractal Rindler-Regge Triangulation in the Hyperbolic Plane and Cosmic de Sitter Accelerated Expansion. Journal of Quantum Information Science, 5, 24-31. http://dx.doi.org/10.4236/jqis.2015.51004

[83]   El Naschie, M.S. (2015) The Casimir Topological Effect and a Proposal for a Casimir-Dark Energy Nano Reactor. World Journal of Nano Science and Engineering, 5, 26-33. http://dx.doi.org/10.4236/wjnse.2015.51004

[84]   El Naschie, M.S. (2014) From Highly Structured E-Infinity Rings and Transfinite Maximally Symmetric Manifolds to the Dark Energy Density of the Cosmos. Advances in Pure Mathematics, 4, 641-648. http://dx.doi.org/10.4236/apm.2014.412073

[85]   Binnig, G. (1990) Ausdem Nichits: über die Kreativitat von Natur und Mensch. Piper Verlag, Munich, Germany.

[86]   ‘tHooft, G. (1997) In Search of the Ultimate Building Blocks. Cambridge University Press, Cambridge.

[87]   Susskind, L. (2010) An Introduction to the Holographic Universe—Black Holes, Information and the String Theory Revolution. World Scientific, Singapore.

[88]   McKeon, D.G. and Ord, G.N. (1992) Time Reversal in Stochastic Processes and Dirac Equation. Physics Review Letters, 69, 3-4. http://dx.doi.org/10.1103/PhysRevLett.69.3