1,130 research outputs found
Simple sufficient conditions for the generalized covariant entropy bound
The generalized covariant entropy bound is the conjecture that the entropy of
the matter present on any non-expanding null hypersurface L will not exceed the
difference between the areas, in Planck units, of the initial and final spatial
2-surfaces bounding L. The generalized Bekenstein bound is a special case which
states that the entropy of a weakly gravitating isolated matter system will not
exceed the product of its mass and its width. Here we show that both bounds can
be derived directly from the following phenomenological assumptions: that
entropy can be computed by integrating an entropy current which vanishes on the
initial boundary and whose gradient is bounded by the energy density. Though we
note that any local description of entropy has intrinsic limitations, we argue
that our assumptions apply in a wide regime. We closely follow the framework of
an earlier derivation, but our assumptions take a simpler form, making their
validity more transparent in some examples.Comment: 7 pages, revte
The Holographic Principle for General Backgrounds
We aim to establish the holographic principle as a universal law, rather than
a property only of static systems and special space-times. Our covariant
formalism yields an upper bound on entropy which applies to both open and
closed surfaces, independently of shape or location. It reduces to the
Bekenstein bound whenever the latter is expected to hold, but complements it
with novel bounds when gravity dominates. In particular, it remains valid in
closed FRW cosmologies and in the interior of black holes. We give an explicit
construction for obtaining holographic screens in arbitrary space-times (which
need not have a boundary). This may aid the search for non-perturbative
definitions of quantum gravity in space-times other than AdS.Comment: 15 pages, 4 figures. Based on a talk given at Strings '99. Includes a
reply to recent criticism. For more details, examples, and references, see
hep-th/9905177 and hep-th/990602
Light Sheets and the Covariant Entropy Conjecture
We examine the holography bound suggested by Bousso in his covariant entropy
conjecture, and argue that it is violated because his notion of light sheet is
too generous. We suggest its replacement by a weaker bound.Comment: 5 pages, to appear in Classical and Quantum Gravit
A covariant entropy bound conjecture on the dynamical horizon
As a compelling pattern for the holographic principle, our covariant entropy
bound conjecture is proposed for more general dynamical horizons. Then we apply
our conjecture to CDM cosmological models, where we find it imposes a
novel upper bound on the cosmological constant for our own universe
by taking into account the dominant entropy contribution from super-massive
black holes, which thus provides an alternative macroscopic perspective to
understand the longstanding cosmological constant problem. As an intriguing
implication of this conjecture, we also discuss the possible profound relation
between the present cosmological constant, the origin of mass, and the
anthropic principle.Comment: JHEP style, 9 pages, 1 figure, honorable mention award received from
Gravity Research Foundation for 2008 Essay Competitio
A covariant entropy conjecture on cosmological dynamical horizon
We here propose a covariant entropy conjecture on cosmological dynamical
horizon. After the formulation of our conjecture, we test its validity in
adiabatically expanding universes with open, flat and closed spatial geometry,
where our conjecture can also be viewed as a cosmological version of the
generalized second law of thermodynamics in some sense.Comment: JHEP style, 9 pages, 1 figure, typos corrected, accepted for
publication in JHE
Quantum Global Structure of de Sitter Space
I study the global structure of de Sitter space in the semi-classical and
one-loop approximations to quantum gravity. The creation and evaporation of
neutral black holes causes the fragmentation of de Sitter space into
disconnected daughter universes. If the black holes are stabilized by a charge,
I find that the decay leads to a necklace of de Sitter universes (`beads')
joined by near-extremal black hole throats. For sufficient charge, more and
more beads keep forming on the necklace, so that an unbounded number of
universes will be produced. In any case, future infinity will not be connected.
This may have implications for a holographic description of quantum gravity in
de Sitter space.Comment: 37 pages, LaTeX2e, 10 figures. v2: references adde
Probing entropy bounds with scalar field spacetimes
We study covariant entropy bounds in dynamical spacetimes with naked
singularities. Specifically we study a spherically symmetric massless scalar
field solution. The solution is an inhomogeneous cosmology with an initial
spacelike singularity, and a naked timelike singularity at the origin. We
construct the entropy flux 4-vector for the scalar field, and show by explicit
computation that the generalized covariant bound is violated for light sheets in the neighbourhood of the (evolving)
apparent horizon. We find no violations of the Bousso bound (for which
), even though certain sufficient conditions for this bound do not
hold. This result therefore shows that these conditions are not necessary.Comment: 10 pages, 5 figures; published version with typos correcte
Holographic Domains of Anti-de Sitter Space
An AdS_4 brane embedded in AdS_5 exhibits the novel feature that a
four-dimensional graviton is localized near the brane, but the majority of the
infinite bulk away from the brane where the warp factor diverges does not see
four-dimensional gravity. A naive application of the holographic principle from
the point of view of the four-dimensional observer would lead to a paradox; a
global holographic mapping would require infinite entropy density. In this
paper, we show that this paradox is resolved by the proper covariant
formulation of the holographic principle. This is the first explicit example of
a time-independent metric for which the spacelike formulation of the
holographic principle is manifestly inadequate. Further confirmation of the
correctness of this approach is that light-rays leaving the brane intersect at
the location where we expect four-dimensional gravity to no longer dominate. We
also present a simple method of locating CFT excitations dual to a particle in
the bulk. We find that the holographic image on the brane moves off to infinity
precisely when the particle exits the brane's holographic domain. Our analysis
yields an improved understanding of the physics of the AdS_4/AdS_5 model.Comment: 29 pages, 6 figure
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