The Entropy of a Vacuum: What Does the Covariant Entropy Count?

Abstract

We argue that a unitary description of the formation and evaporation of a black hole implies that the Bekenstein-Hawking entropy is the "entropy of a vacuum": the logarithm of the number of possible independent ways in which quantum field theory on a fixed classical spacetime background can emerge in a full quantum theory of gravity. In many cases, the covariant entropy counts this entropy--the degeneracy of emergent quantum field theories in full quantum gravity--with the entropy of particle excitations in each quantum field theory giving only a tiny perturbation. In the Rindler description of a (black hole) horizon, the relevant vacuum degrees of freedom manifest themselves as an extra hidden quantum number carried by the states representing the second exterior region; this quantum number is invisible in the emergent quantum field theory. In a distant picture, these states arise as exponentially degenerate ground and excited states of the intrinsically quantum gravitational degrees of freedom on the stretched horizon. The formation and evaporation of a black hole involve processes in which the entropy of collapsing matter is transformed into that of a vacuum and then to that of final-state Hawking radiation. In the intermediate stage of this evolution, entanglement between the vacuum and (early) Hawking radiation develops, which is transferred to the entanglement among final-state Hawking quanta through the evaporation process. The horizon is kept smooth throughout the evolution; in particular, no firewall develops. Similar considerations also apply for cosmological horizons, for example for the horizon of a meta-stable de-Sitter space.

30 pages; v2: references added, minor revisions; v3: footnotes 2 and 7 added for the journal version

References in corpus (12)

• Black holes as mirrors: quantum information in random subsystems
• State-Dependent Bulk-Boundary Maps and Black Hole Complementarity
• Gauge/Gravity Duality and the Black Hole Interior
• The Black Hole Interior in AdS/CFT and the Information Paradox
• Black Holes, Information, and Hilbert Space for Quantum Gravity
• Firewalls From Double Purity
• Passing through the Firewall
• Black Holes or Firewalls: A Theory of Horizons
• Black Hole Information as Topological Qubits
• Saturating the holographic entropy bound
• Black Holes, Entropies, and Semiclassical Spacetime in Quantum Gravity
• Cool horizons lead to information loss

Cited by in corpus (15)

• Constraints on the Generalized Uncertainty Principle from Black Hole Thermodynamics
• Excluding Black Hole Firewalls with Extreme Cosmic Censorship
• Toward a Holographic Theory for General Spacetimes
• The Black Hole Interior in Quantum Gravity
• Reanalyzing an Evaporating Black Hole
• Spacetime Equals Entanglement
• The Boundary Dual of Bulk Local Operators
• Black Hole and de Sitter Microstructures from a Semiclassical Perspective
• Black Holes, Entropies, and Semiclassical Spacetime in Quantum Gravity
• Why Firewalls Need Not Exist
• Entanglement Entropy in the $\sigma$-Model with the de Sitter Target Space
• Unitary description of the black hole by prime numbers
• Flat-space Quantum Gravity in AdS/CFT
• Entanglement of Vacuum States With the de Sitter Horizon: Consequences on Holographic Dark Energy
• Holographic Shannon Entropy: The Outer Entropy of Entanglement Wedges