Black hole entropy quantization

TL;DR

This paper explores how loop quantum gravity can align with Bekenstein's proposal of quantized black hole entropy, despite not having equidistant area quantization, by analyzing microstates and entropy-area oscillations.

Contribution

It demonstrates that non-equidistant area spectra in loop quantum gravity can still produce an effectively quantized entropy consistent with Bekenstein's hypothesis.

Findings

Loop quantum gravity's area spectrum is not equidistant.

Oscillatory behavior in entropy-area relation can be interpreted to support quantized entropy.

Consistency with Bekenstein's entropy quantization is achieved through microstate analysis.

Abstract

Ever since the pioneer works of Bekenstein and Hawking, black hole entropy has been known to have a quantum origin. Furthermore, it has long been argued by Bekenstein that entropy should be quantized in discrete (equidistant) steps given its identification with horizon area in (semi-)classical general relativity and the properties of area as an adiabatic invariant. This lead to the suggestion that black hole area should also be quantized in equidistant steps to account for the discrete black hole entropy. Here we shall show that loop quantum gravity, in which area is {\it not} quantized in equidistant steps can nevertheless be consistent with Bekenstein's equidistant entropy proposal in a subtle way. For that we perform a detailed analysis of the number of microstates compatible with a given area and show consistency with the Bekenstein framework when an oscillatory behavior in the entropy-area relation is properly interpreted.