Abstract
The covariant entropy bound states that the entropy, , of matter on a light sheet cannot exceed a quarter of its initial area, , 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, , may hold true. In this note, we exhibit light sheets whose entropy exceeds 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 (), and not as had hitherto been believed. Our results strengthen the evidence for the covariant entropy bound, while showing that the stronger bound is not universally valid. We conjecture that the stronger bound does hold for static, weakly gravitating systems.
3 More- Received 9 June 2010
DOI:https://doi.org/10.1103/PhysRevD.82.084024
© 2010 The American Physical Society