TY - JOUR

T1 - From Planck area to graph theory

T2 - Topologically distinct black hole microstates

AU - Davidson, Aharon

N1 - Publisher Copyright:
© 2019 American Physical Society.

PY - 2019/10/18

Y1 - 2019/10/18

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85074342767&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.100.081502

DO - 10.1103/PhysRevD.100.081502

M3 - Article

AN - SCOPUS:85074342767

SN - 2470-0010

VL - 100

JO - Physical Review D

JF - Physical Review D

IS - 8

M1 - 081502

ER -