Black Holes and Entropy

TLDR

Black‑hole physics shares key thermodynamic features, notably that both black‑hole area and entropy increase irreversibly. The study proposes a thermodynamic framework for black‑hole physics grounded in the area–entropy analogy. The authors review information‑theoretic concepts and apply them to black‑hole physics to formulate a thermodynamic description. They define black‑hole entropy as the inaccessible information about the interior, show it equals area divided by the Planck length squared up to an order‑unity constant, and demonstrate that a generalized second law—total entropy never decreases when matter falls into a black hole—is upheld by information‑theoretic arguments and examples.

Abstract

There are a number of similarities between black-hole physics and thermodynamics. Most striking is the similarity in the behaviors of black-hole area and of entropy: Both quantities tend to increase irreversibly. In this paper we make this similarity the basis of a thermodynamic approach to black-hole physics. After a brief review of the elements of the theory of information, we discuss black-hole physics from the point of view of information theory. We show that it is natural to introduce the concept of black-hole entropy as the measure of information about a black-hole interior which is inaccessible to an exterior observer. Considerations of simplicity and consistency, and dimensional arguments indicate that the black-hole entropy is equal to the ratio of the black-hole area to the square of the Planck length times a dimensionless constant of order unity. A different approach making use of the specific properties of Kerr black holes and of concepts from information theory leads to the same conclusion, and suggests a definite value for the constant. The physical content of the concept of black-hole entropy derives from the following generalized version of the second law: When common entropy goes down a black hole, the common entropy in the black-hole exterior plus the black-hole entropy never decreases. The validity of this version of the second law is supported by an argument from information theory as well as by several examples.