A Covariant Entropy Conjecture

Abstract

We conjecture the following entropy bound to be valid in all space-times admitted by Einstein's equation: Let A be the area of any two-dimensional surface. Let L be a hypersurface generated by surface-orthogonal null geodesics with non-positive expansion. Let S be the entropy on L. Then S does not exceed A/4. We present evidence that the bound can be saturated, but not exceeded, in cosmological solutions and in the interior of black holes. For systems with limited self-gravity it reduces to Bekenstein's bound. Because the conjecture is manifestly time reversal invariant, its origin cannot be thermodynamic, but must be statistical. Thus it places a fundamental limit on the number of degrees of freedom in nature.

41 pages, 7 figures. v2,v3: references added

References in corpus (2)

• On Holography and Cosmology
• The Generalized Second Law of Thermodynamics in Cosmology

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• A violation of the covariant entropy bound?
• D3 branes in a Melvin universe: a new realm for gravitational holography
• The Bousso entropy bound in selfgravitating gas of massless particles
• Recovering semiclassical Einstein's equation using generalized entropy
• A covariant entropy bound conjecture on the dynamical horizon
• A bound system in the expanding universe with modified holographic Ricci dark energy and dark matter
• Universal entropy relations: entropy formulae and entropy bound
• Does the Holographic Principle determine the Gravitational Interaction?
• Constraints on physical computers in holographic spacetimes
• Realize Emergent Gravity to Generic Situations
• Quantum fluctuations of the compact phase space cosmology
• Gravity as a thermodynamic phenomenon
• Quantum Bias Cosmology: Acceleration from Holographic Information Capacity
• Entropy Bounds and Holographic Dark Energy: Conflicts and Consensus
• A non-singular closed bouncing universe without violation of null energy condition
• Holographic phenomenology via overlapping degrees of freedom
• Holographic temperature bound in the slow-roll inflation
• Quantum Mechanics, Gravity, and the Multiverse
• Thoughts on Big Bang
• A domain wall bound on anti-de Sitter vacua
• Covariant odd entanglement entropy in AdS${}_3$/CFT${}_2$
• The generalized second law for fermionic and bosonic fields
• Holography: 2-D or not 2-D?
• Locality and the classical limit of quantum mechanics
• Twistors and Holography
• On the assumptions leading to the information loss paradox
• Entropy and Black Holes in the Very Early Universe
• Random versus holographic fluctuations of the background metric. II. Note on the dark energies arising due to microstructure of space-time
• Singularities From Entropy
• Spacetime granularity from finite-dimensionality of local observable algebras
• Violation of the KSS Bound in Holographic Bjorken-Flow
• A fluid of black holes at the beginning of the Universe
• Flat-space Quantum Gravity in AdS/CFT
• An operational view on the holographic information bound
• Holographic Equipartition and Gravitational Collapse
• Holography for a small world
• Precision Cosmology and the Landscape
• Covariant entropy conjecture and concordance cosmological models
• Isentropic processes for axisymmetric Black Holes
• Dynamical Horizon Entropy Bound Conjecture in Loop Quantum Cosmology
• Hamilton-Jacobi equation and the breaking of the WKB approximation
• The Relativity of Existence
• Holography, Dimensional Reduction and the Bekenstein Bound
• A Holographic Holographic Bound and the Black Hole S-Matrix
• On Emergent Geometry from Entanglement Entropy in Matrix theory
• Finite Matter Resolution of the Cosmological Entropy Problem
• Probing sine dilaton gravity with flow central charge
• Nonperturbative Isentropic Processes in AdS Black Holes with Nonlinear Electrodynamics
• An Entropy-Based Criterion for Geodesic Incompleteness
• Background instability of quintessence model in light of entropy and distance conjecture
• The Quantum and Statistical Theory of Early Universe and Its Possible Applications to Cosmology
• Energy Momentum Tensor Correlators in Improved Holographic QCD
• Lightsheets, Branes and the Covariant Entropy Bound
• Holography for de Sitter bubble geometries
• Breaking Free from the Swampland of Impossible Universes through the DESI Portal
• Holographic Shannon Entropy: The Outer Entropy of Entanglement Wedges
• Black Hole Mergers as the Fastest Photon Ring Scramblers
• Entropy of Causal Horizons
• Numerical Relativity, Holography and the Quantum Null Energy Condition
• Holographic c-Function
• Holographic Space-time and Quantum Information
• Physical Relativism as an Interpretation of Existence
• Non-relativistic geometry of holographic screens
• Bousso's Covariant Entropy Bound and Padmanabhan's Emergent Universe
• Perturbations In Some Dark Energy Models