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

Understand

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.