1,210 research outputs found
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
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