Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Black Holes as Markers of Dimensionality

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

How to cite: Łukaszyk, S. Black Holes as Markers of Dimensionality. Preprints 2021, 2021090368 (doi: 10.20944/preprints202109.0368.v1). Łukaszyk, S. Black Holes as Markers of Dimensionality. Preprints 2021, 2021090368 (doi: 10.20944/preprints202109.0368.v1).

Abstract

Black hole temperature as a function of its Planck length diameter multiple is derived from black hole surface gravity and Hawking temperature. It is conjectured that this multiple corresponds to dimensionality of the graph of nature with d = 1/2pi describing primordial Big Bang singularity. 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 -c^2 if all its vertices have black hole gravitational potential of -c^2/2 and is inactive otherwise. Temporary distribution of active triangles on an event horizon tends to maximize Shannon entropy. 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 a diameter. A similarity of the logistic function and black hole FD statistics leads to the BE logistic function and map. 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

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