Black Hole Entropy: From Shannon to Bekenstein

TL;DR

This paper derives the Bekenstein-Hawking black hole entropy using Shannon's information theory, linking quantum near-horizon modes with classical entropy in a semi-classical framework.

Contribution

It introduces a semi-classical approach applying Shannon entropy to black hole horizons using quantum mode functions, connecting information theory with black hole thermodynamics.

Findings

Black hole entropy can be derived from Shannon's formula.

Quantum near-horizon modes inform the tunneling probability.

The approach supports the information theoretic origin of black hole entropy.

Abstract

In this note we have applied directly the Shannon formula for information theory entropy to derive the Black Hole (Bekenstein-Hawking) entropy. Our analysis is semi-classical in nature since we use the (recently proposed [8]) quantum mechanical near horizon mode functions to compute the tunneling probability that goes in to the Shannon formula, following the general idea of [5]. Our framework conforms to the information theoretic origin of Black Hole entropy, as originally proposed by Bekenstein.