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# Black Holes as Markers of Dimensionality

Version 1
: Received: 20 September 2021 / Approved: 21 September 2021 / Online: 21 September 2021 (14:51:37 CEST)

Version 2 : Received: 24 November 2021 / Approved: 25 November 2021 / Online: 25 November 2021 (11:12:36 CET)

Version 2 : Received: 24 November 2021 / Approved: 25 November 2021 / Online: 25 November 2021 (11:12:36 CET)

How to cite:
Łukaszyk, S. Black Holes as Markers of Dimensionality. *Preprints* **2021**, 2021090368 (doi: 10.20944/preprints202109.0368.v2).
Łukaszyk, S. Black Holes as Markers of Dimensionality. Preprints 2021, 2021090368 (doi: 10.20944/preprints202109.0368.v2).

## Abstract

Black hole temperature

*T*=_{BH}*T*/2_{P}*π**d*as a function of its Planck length real diameter multiplier*d*is derived from black hole surface gravity and Hawking temperature w.l.o.g. It is conjectured*d*= 1/2*π*describes primordial Big Bang singularity as in this case*T*=_{BH}*T*. A black hole interacts with the environment and observable black holes have uniquely defined Delaunay triangulations with a natural number of spherical triangles having Planck areas (bits), where a Planck triangle is active and has gravitational potential of -_{P}*c*^{2}if all its vertices have black hole gravitational potential of -*c*^{2}/2 and is inactive otherwise. As temporary distribution of active triangles on an event horizon tends to maximize Shannon entropy a black hole is a fundamental, one-sided thermodynamic equilibrium limit for a dissipative structure. Black hole blackbody radiation, informational capacity fluctuations, and quantum statistics are discussed. On the basis of the latter, wavelength bounds for BE, MB, and FD statistics are derived as a function of the diameter multiplier*d*. It is shown that black holes feature wave-particle duality only if*d*≤ 8*π*, which also sets the maximum diameter of a totally collapsible black hole. This outlines the program for research of other nature phenomena that emit perfect blackbody radiation, such as neutron stars and white dwarfs.## Keywords

quantum black holes; entropic gravity; the black hole information paradox; Shannon entropy; Delaunay triangulation; black hole quantum statistics; logistic function/map; exotic ℝ4

## Subject

PHYSICAL SCIENCES, Mathematical Physics

Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Commenter: Szymon Łukaszyk

Commenter's Conflict of Interests: Author

i.2. Every dissipative structure is bounded by (2+

i)-dimensional topological sphere.3. Black holes are fundamental, one-sided thermodynamic equilibrium limits for dissipative structures.

4. Discretizing mass, wavelength and diameter using multiplieres

m,l,dand Planck units to arrive atl=2π/mformula for Compton wavelength.5. Constraining to 1≤

larriving at the black hole vawe-particle duality bound d≤8π.

6. Obtaining the same bound d≤8πfor a black hole colapse on the basis of black hole emission formula.etc.