How Objective is Black Hole Entropy?

TL;DR

This paper examines the objectivity of black hole entropy, proposing it as an observer-dependent measure of information consistent with thermodynamics, especially in the semiclassical limit where metric fluctuations are negligible.

Contribution

It introduces an information-theoretic interpretation of black hole entropy using Jaynes' maximum entropy principle and Euclidean path integrals, linking entropy to observer knowledge.

Findings

Black hole entropy equals maximal information entropy in the semiclassical limit.

Black hole entropy is observer-dependent and related to the observer's knowledge.

In the negligible fluctuation limit, entropy measures internal mass eigenstates.

Abstract

The objectivity of black hole entropy is discussed in the particular case of a Schwarzchild black hole. Using Jaynes' maximum entropy formalism and Euclidean path integral evaluation of partition function, it is argued that in the semiclassical limit when the fluctutation of metric is neglected, the black hole entropy of a Schwarzchild black hole is equal to the maximal information entropy of an observer whose sole knowledge of the black hole is its mass. Black hole entropy becomes a measure of number of its internal mass eigenstates in accordance with the Boltzmann principle only in the limit of negligible relative mass fluctutation. {}From the information theoretic perspective, the example of a Schwarzchild black hole seems to suggest that black hole entropy is no different from ordinary thermodynamic entropy. It is a property of the experimental data of a black hole, rather than being an intrinsic physical property of a black hole itself independent of any observer. However, it is still weakly objective in the sense that different observers given the same set of data of a black hole will measure the same maximal information entropy.