Evidence for an entropy bound from fundamentally discrete gravity

Abstract

The various entropy bounds that exist in the literature suggest that spacetime is fundamentally discrete, and hint at an underlying relationship between geometry and "information". The foundation of this relationship is yet to be uncovered, but should manifest itself in a theory of quantum gravity. We present a measure for the maximal entropy of spherically symmetric spacelike regions within the causal set approach to quantum gravity. In terms of the proposal, a bound for the entropy contained in this region can be derived from a counting of potential "degrees of freedom" associated to the Cauchy horizon of its future domain of dependence. For different spherically symmetric spacelike regions in Minkowski spacetime of arbitrary dimension, we show that this proposal leads, in the continuum approximation, to Susskind's well-known spherical entropy bound.

25 pages, 9 figures. Comment on Bekenstein bound added and smaller corrections. To be published in Class.Quant.Grav

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Cited by in corpus (17)

• Black Hole Thermodynamics
• The causal set approach to quantum gravity
• Particle propagators on discrete spacetime
• Spacelike distance from discrete causal order
• Symmetries, Horizons, and Black Hole Entropy
• Stable Homology as an Indicator of Manifoldlikeness in Causal Set Theory
• Black Hole Thermodynamics and Statistical Mechanics
• Emergence of spatial structure from causal sets
• Causal Sets: Quantum gravity from a fundamentally discrete spacetime
• Black Hole Thermodynamics from Euclidean Horizon Constraints
• Black Hole Entropy and the Problem of Universality
• Black Hole Entropy and the Problem of Universality
• A Causal Set Black Hole
• The black hole dynamical horizon and generalized second law of thermodynamics
• Horizon thermodynamics in $f(R,R^{\mu \nu }{R}_{\mu \nu })$ theory
• Covariant entropy conjecture and concordance cosmological models
• Black holes and singularities in causal set gravity