Spectrum of quantized black hole, correspondence principle, and holographic bound

TL;DR

This paper examines the spectrum of quantized black holes, revealing inconsistencies with the holographic bound and the correspondence principle, and discusses conditions under which black hole entropy aligns with holographic principles.

Contribution

It demonstrates that an equidistant horizon area spectrum conflicts with fundamental principles unless specific conditions are met in loop quantum gravity.

Findings

Equidistant spectrum does not follow from the correspondence principle.

LQG spectrum either violates the holographic bound or requires a special Barbero-Immirzi parameter.

Partial distinguishability of edges allows entropy to be proportional to area and satisfy the holographic bound.

Abstract

An equidistant spectrum of the horizon area of a quantized black hole does not follow from the correspondence principle or from general statistical arguments. On the other hand, such a spectrum obtained in loop quantum gravity (LQG) either does not comply with the holographic bound, or demands a special choice of the Barbero-Immirzi parameter for the horizon surface, distinct from its value for other quantized surfaces. The problem of distinguishability of edges in LQG is discussed, with the following conclusion. Only under the assumption of partial distinguishability of the edges, the microcanonical entropy of a black hole can be made both proportional to the horizon area and satisfying the holographic bound.