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 metastable de Sitter space.

• Received 4 November 2013

DOI:https://doi.org/10.1103/PhysRevD.90.104003