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.
Highlights
It would be intuitively reasonable to suppose that in the case of black holes [1]-[10] with high dimensionality, i.e. extra dimensions [8], the horizon i.e. the hyper quasi surface of the black hole horizon will be of higher dimensionality
Dvoretzky [16] [17] leads to the definite conclusion that in sufficiently high dimensional spaces such as our quantum spacetime [12]-[14], about 96% of the volume resides on the surface or very near to it while a near to only 4% remains in the deceptive bulk [16] [17]
The moral which we can learn, relearn from this theorem is a well known wisdom from many counterintuitive results of geometry in higher dimensions, namely that we should in general never generalize an obvious conclusion from a low dimensional space to a higher one
Summary
It would be intuitively reasonable to suppose that in the case of black holes [1]-[10] with high dimensionality, i.e. extra dimensions [8], the horizon i.e. the hyper quasi surface of the black hole horizon will be of higher dimensionality. It would seem to follow that the information that resides only on the surface will be, so to speak, diluted because the Bekenstein limit is supposed to remain the same [1] [3]. (2015) The Counterintuitive Increase of Information Due to Extra Spacetime Dimensions of a Black Hole and Dvoretzky’s Theorem. Dvoretzky [16] [17] leads to the definite conclusion that in sufficiently high dimensional spaces such as our quantum spacetime [12]-[14], about 96% of the volume resides on the surface or very near to it while a near to only 4% remains in the deceptive bulk [16] [17]. It is thought that in this form the Bekenstein real limit on information will become topological and measure theoretical universality which dispels the black hole information paradox [6] [7] [11] [12] in an unheard of simplicity conserving the most important feature of the theory of Hawking on the one side and ‘tHooft-Susskind on the other without violating any fundamental laws of physics [11] [12]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
