The Counterintuitive Increase of Information Due to Extra Spacetime Dimensions of a Black Hole and Dvoretzky’s Theorem
Author(s)
Mohamed S. El Naschie*
ABSTRACT
As per Hawking and Bekenstein’s work on black holes, information resides on the surface and there is a limit on it amounting to a bit for every Planck area. It would seem therefore that extra dimensions would logically lead to a hyper-surface for a black hole and consequently a reduction of the corresponding information density due to the dilution effect of these additional dimensions. The present paper argues that the counterintuitive opposite of the above is what should be expected. This surprising result is a consequence of a well known theorem on measure concentration due to I. Dvoretzky.
As per Hawking and Bekenstein’s work on black holes, information resides on the surface and there is a limit on it amounting to a bit for every Planck area. It would seem therefore that extra dimensions would logically lead to a hyper-surface for a black hole and consequently a reduction of the corresponding information density due to the dilution effect of these additional dimensions. The present paper argues that the counterintuitive opposite of the above is what should be expected. This surprising result is a consequence of a well known theorem on measure concentration due to I. Dvoretzky.
KEYWORDS
Higher Dimensional Black Holes, Dvoretzky’s Theorem, Information Paradox, E-Infinity Theory, Counterintuitive Geometry, Bekenstein Limit, Hawking Radiation, ‘tHooft-Susskind Black Holes
Higher Dimensional Black Holes, Dvoretzky’s Theorem, Information Paradox, E-Infinity Theory, Counterintuitive Geometry, Bekenstein Limit, Hawking Radiation, ‘tHooft-Susskind Black Holes
Cite this paper
El Naschie, M. (2015) The Counterintuitive Increase of Information Due to Extra Spacetime Dimensions of a Black Hole and Dvoretzky’s Theorem. Natural Science, 7, 483-487. doi: 10.4236/ns.2015.710049.
El Naschie, M. (2015) The Counterintuitive Increase of Information Due to Extra Spacetime Dimensions of a Black Hole and Dvoretzky’s Theorem. Natural Science, 7, 483-487. doi: 10.4236/ns.2015.710049.
References
[1] Frolov, V.P. and Zelnikov, A. (2011) Introduction to Black Hole Physics. Oxford University Press, Oxford, UK.
http://dx.doi.org/10.1093/acprof:oso/9780199692293.001.0001 [2] Bardeen, J.M., Carter, B. and Hawking, S.W. (1973) The Four Laws of Black Hole Mechanics. Communications in Mathematical Physics, 31, 161-170.
http://dx.doi.org/10.1007/BF01645742 [3] Bekenstein, J.D. (1980) Black Hole Thermodynamics. Physics Today, 33, 24-31.
http://dx.doi.org/10.1063/1.2913906 [4] Meisner, C.W., Thorne, K.S. and Wheeler, J.A. (1973) Gravitation. W.H. Freeman & Company, San Francisco. [5] Weinberg, S. (2008) Cosmology. Oxford University Press, Oxford, UK. [6] Susskind, L. and Lindesay, J. (2005) Black Holes, Information and the String Theory Revolution (The Holographic Universe). World Scientific, New Jersey. [7] Susskind, L. (2008) The Black Hole War. Back Bay Books, New York. [8] Horowitz, G.T. (Ed.) (2012) Black Holes in Higher Dimensions. Cambridge University Press, Cambridge, UK.
http://dx.doi.org/10.1017/CBO9781139004176 [9] Wheeler, A. (1990) Information, Physics, Quantum: The Search for Links. In: Zurek, W., Ed., Complexity Entropy and the Physics of Information, Addison-Wesley, New York, 3-18. [10] G. ‘tHooft (2015) G. ‘tHooft Asks a Question about General Relativity on ResearchGate, Questions and Answers, October.
https://www.researchgate.net/post/In_GR_can_we_always_choose_the_local_speed_of_light_to_be
_everywhere_smaller_that_the_coordinate_speed_of_light_Can_this_be_used_in_a_theory [11] El Naschie, M.S. (2006) Fractal Black Holes and Information. Chaos, Solitons & Fractals, 29, 23-35.
http://dx.doi.org/10.1016/j.chaos.2005.11.079 [12] El Naschie, M.S. (2015) If Quantum “Wave” of the Universe Then Quantum “Particle” of the Universe: A Resolution of the Dark Energy Question and the Black Hole Information Paradox. International Journal of Astronomy & Astrophysics, 5, 243-247.
http://dx.doi.org/10.4236/ijaa.2015.54027 [13] El Naschie, M.S. (2015) A Resolution of the Black Hole Information Paradox via Transfinite Set Theory. World Journal of Condensed Matter Physics, 5, 249-260.
http://dx.doi.org/10.4236/wjcmp.2015.54026 [14] El Naschie, M.S. (2004) A Review of E-Infinity 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 [15] Connes, A. (1994) Noncommutative Geometry. Academic Press, San Diego. [16] Levy, S. (Ed.) (1997) Flavors of Geometry. Cambridge University Press, Cambridge, UK. [17] 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.
http://dx.doi.org/10.11648/j.ijhep.20150201.12 [18] El Naschie, M.S. (2015) Kerr Black Hole Geometry Leading to Dark Matter and Dark Energy via E-Infinity Theory and the Possibility of Nano Spacetime Singularity Reactor. Natural Science, 7, 210-225.
http://dx.doi.org/10.4236/ns.2015.74024
[1] Frolov, V.P. and Zelnikov, A. (2011) Introduction to Black Hole Physics. Oxford University Press, Oxford, UK.
http://dx.doi.org/10.1093/acprof:oso/9780199692293.001.0001 [2] Bardeen, J.M., Carter, B. and Hawking, S.W. (1973) The Four Laws of Black Hole Mechanics. Communications in Mathematical Physics, 31, 161-170.
http://dx.doi.org/10.1007/BF01645742 [3] Bekenstein, J.D. (1980) Black Hole Thermodynamics. Physics Today, 33, 24-31.
http://dx.doi.org/10.1063/1.2913906 [4] Meisner, C.W., Thorne, K.S. and Wheeler, J.A. (1973) Gravitation. W.H. Freeman & Company, San Francisco. [5] Weinberg, S. (2008) Cosmology. Oxford University Press, Oxford, UK. [6] Susskind, L. and Lindesay, J. (2005) Black Holes, Information and the String Theory Revolution (The Holographic Universe). World Scientific, New Jersey. [7] Susskind, L. (2008) The Black Hole War. Back Bay Books, New York. [8] Horowitz, G.T. (Ed.) (2012) Black Holes in Higher Dimensions. Cambridge University Press, Cambridge, UK.
http://dx.doi.org/10.1017/CBO9781139004176 [9] Wheeler, A. (1990) Information, Physics, Quantum: The Search for Links. In: Zurek, W., Ed., Complexity Entropy and the Physics of Information, Addison-Wesley, New York, 3-18. [10] G. ‘tHooft (2015) G. ‘tHooft Asks a Question about General Relativity on ResearchGate, Questions and Answers, October.
https://www.researchgate.net/post/In_GR_can_we_always_choose_the_local_speed_of_light_to_be
_everywhere_smaller_that_the_coordinate_speed_of_light_Can_this_be_used_in_a_theory [11] El Naschie, M.S. (2006) Fractal Black Holes and Information. Chaos, Solitons & Fractals, 29, 23-35.
http://dx.doi.org/10.1016/j.chaos.2005.11.079 [12] El Naschie, M.S. (2015) If Quantum “Wave” of the Universe Then Quantum “Particle” of the Universe: A Resolution of the Dark Energy Question and the Black Hole Information Paradox. International Journal of Astronomy & Astrophysics, 5, 243-247.
http://dx.doi.org/10.4236/ijaa.2015.54027 [13] El Naschie, M.S. (2015) A Resolution of the Black Hole Information Paradox via Transfinite Set Theory. World Journal of Condensed Matter Physics, 5, 249-260.
http://dx.doi.org/10.4236/wjcmp.2015.54026 [14] El Naschie, M.S. (2004) A Review of E-Infinity 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 [15] Connes, A. (1994) Noncommutative Geometry. Academic Press, San Diego. [16] Levy, S. (Ed.) (1997) Flavors of Geometry. Cambridge University Press, Cambridge, UK. [17] 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.
http://dx.doi.org/10.11648/j.ijhep.20150201.12 [18] El Naschie, M.S. (2015) Kerr Black Hole Geometry Leading to Dark Matter and Dark Energy via E-Infinity Theory and the Possibility of Nano Spacetime Singularity Reactor. Natural Science, 7, 210-225.
http://dx.doi.org/10.4236/ns.2015.74024