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Black Holes and Entropy

Jacob D. Bekenstein*

  • Joseph Henry Laboratories, Princeton University, Princeton, New Jersey 08540
  • Center for Relativity Theory, The University of Texas at Austin, Austin, Texas 78712

  • *National Science Foundation Predoctoral Fellow when this work was initiated.
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Phys. Rev. D 7, 2333 – Published 15 April, 1973

DOI: https://doi.org/10.1103/PhysRevD.7.2333

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.

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Outline

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Phys. Rev. D 7, 2333– Published 15 April, 1973
  • Received 2 November 1972

© 1973 American Physical Society

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