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arXiv · 1907.03090

From Planck area to graph theory: Topologically distinct black hole microstates

Aharon Davidson
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Abstract

We postulate a Planck scale horizon unit area, with no bits of information locally attached to it, connected but otherwise of free form, and let $n$ such geometric units compactly tile the black hole horizon. Associated with each topologically distinct tiling configuration is then a simple, connected, undirected, unlabeled, planar, chordal graph. The asymptotic enumeration of the corresponding integer sequence gives rise to the Bekenstein-Hawking area entropy formula, automatically accompanied by a proper logarithmic term, and fixes the size of the horizon unit area, thereby constituting a global realization of Wheeler's "it from bit" phrase. Invoking Polya's theorem, an exact number theoretical entropy spectrum is offered for the 2+1 dimensional quantum black hole.

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Aharon Davidson. 2019-07-06. From Planck area to graph theory: Topologically distinct black hole microstates. https://doi.org/10.1103/physrevd.100.081502

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