Saturating the holographic entropy bound

Raphael Bousso, Ben Freivogel, and Stefan Leichenauer
Phys. Rev. D 82, 084024 – Published 13 October 2010

Abstract

The covariant entropy bound states that the entropy, S, of matter on a light sheet cannot exceed a quarter of its initial area, A, in Planck units. The gravitational entropy of black holes saturates this inequality. The entropy of matter systems, however, falls short of saturating the bound in known examples. This puzzling gap has led to speculation that a much stronger bound, SA3/4, may hold true. In this note, we exhibit light sheets whose entropy exceeds A3/4 by arbitrarily large factors. In open Friedmann-Robertson-Walker universes, such light sheets contain the entropy visible in the sky; in the limit of early curvature domination, the covariant bound can be saturated but not violated. As a corollary, we find that the maximum observable matter and radiation entropy in universes with positive (negative) cosmological constant is of order Λ1 (Λ2), and not |Λ|3/4 as had hitherto been believed. Our results strengthen the evidence for the covariant entropy bound, while showing that the stronger bound SA3/4 is not universally valid. We conjecture that the stronger bound does hold for static, weakly gravitating systems.

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  • Received 9 June 2010

DOI:https://doi.org/10.1103/PhysRevD.82.084024

© 2010 The American Physical Society

Authors & Affiliations

Raphael Bousso1,2,3, Ben Freivogel1,2, and Stefan Leichenauer1,2

  • 1Center for Theoretical Physics, Department of Physics University of California, Berkeley, California 94720-7300, USA
  • 2Lawrence Berkeley National Laboratory, Berkeley, California 94720-8162, USA
  • 3Institute for the Physics and Mathematics of the Universe, University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8568, Japan

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Issue

Vol. 82, Iss. 8 — 15 October 2010

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