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

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

The Black Hole Interior in Quantum Gravity

We discuss the interior of a black hole in quantum gravity, in which black holes form and evaporate unitarily. The interior spacetime appears in the sense of complementarity because of special features revealed by the microscopic degrees of freedom when viewed from a semiclassical standpoint. The relation between quantum mechanics and the equivalence principle is subtle, but they are still consistent.Comment: 5 pages; text shortened, references added, Phys. Rev. Lett. in pres

Flat-space Quantum Gravity in AdS/CFT

Motivated by the task of understanding microscopic dynamics of an evolving black hole, we present a scheme describing gauge-fixed continuous time evolution of quantum gravitational processes in asymptotically flat spacetime using the algebra of CFT operators. This allows us to study the microscopic dynamics of the Hawking emission process, although obtaining a full S-matrix may require a modification of the minimal scheme. The role of the operator product expansion is to physically interpret the resulting time evolution by decomposing the Hilbert space of the states for the entire system into those for smaller subsystems. We translate the picture of an evaporating black hole previously proposed by the authors into predictions for nonperturbative properties of the CFTs that have weakly coupled dual gravitational descriptions. We also discuss a possible relationship between the present scheme and a reference frame change in the bulk.Comment: 31 pages, 2 figures; clarifications adde

Black Holes or Firewalls: A Theory of Horizons

We present a quantum theory of black hole (and other) horizons, in which the standard assumptions of complementarity are preserved without contradicting information theoretic considerations. After the scrambling time, the quantum mechanical structure of a black hole becomes that of an eternal black hole at the microscopic level. In particular, the stretched horizon degrees of freedom and the states entangled with them can be mapped into the near-horizon modes in the two exterior regions of an eternal black hole, whose mass is taken to be that of the evolving black hole at each moment. Salient features arising from this picture include: (i) the number of degrees of freedom needed to describe a black hole is e^{A/2 l_P^2}, where A is the area of the horizon; (ii) black hole states having smooth horizons span only an e^{A/4 l_P^2}-dimensional subspace of the relevant e^{A/2 l_P^2}-dimensional Hilbert space; (iii) internal dynamics of the horizon is such that an infalling observer finds a smooth horizon with probability 1 if a state stays in this subspace. We identify the structure of local operators in the exterior and interior spacetime regions, and show that this structure avoids firewall arguments---the horizon can keep being smooth throughout the evolution. We discuss the fate of falling observers under various circumstances, especially when they manipulate degrees of freedom before entering the horizon, and find that an observer can never see a firewall by making a measurement on early Hawking radiation. We also consider the framework in an infalling reference frame, and argue that Minkowski-like vacua are not unique. In particular, the number of true Minkowski vacua is infinite, although the label discriminating these vacua cannot be accessed in usual non-gravitational quantum field theory. An application to de Sitter horizons is also discussed.Comment: 24 pages, 1 figure; minor revision

Low Energy Description of Quantum Gravity and Complementarity

We consider a framework in which low energy dynamics of quantum gravity is described preserving locality, and yet taking into account the effects that are not captured by the naive global spacetime picture, e.g. those associated with black hole complementarity. Our framework employs a "special relativistic" description of gravity; specifically, gravity is treated as a force measured by the observer tied to the coordinate system associated with a freely falling local Lorentz frame. We identify, in simple cases, regions of spacetime in which low energy local descriptions are applicable as viewed from the freely falling frame; in particular, we identify a surface called the gravitational observer horizon on which the local proper acceleration measured in the observer's coordinates becomes the cutoff (string) scale. This allows for separating between the "low-energy" local physics and "trans-Planckian" intrinsically quantum gravitational (stringy) physics, and allows for developing physical pictures of the origins of various effects. We explore the structure of the Hilbert space in which the proposed scheme is realized in a simple manner, and classify its elements according to certain horizons they possess. We also discuss implications of our framework on the firewall problem. We conjecture that the complementarity picture may persist due to properties of trans-Planckian physics.Comment: 18 pages, 1 figure; matches published versio