260 research outputs found
Techniques to collect and analyze the cognitive map knowledge of persons with visual impairment or blindness: issues of validity
This article is an assessment of a variety of techniques used by researchers
in the fields of geography, psychology, urban planning, and cognitive science to collect
and analyze data on how people with visual impairment or blindness learn,
understand, and think about geographic space. The authors concluded that these techniques
and their results need to be used cautiously. They also made recommendations
for increasing the validity of future studies, including the use of multiple, mutually
supportive tests; larger sample sizes, and movement from the laboratory to real-world
environments
Quantum field theory on a growing lattice
We construct the classical and canonically quantized theories of a massless
scalar field on a background lattice in which the number of points--and hence
the number of modes--may grow in time. To obtain a well-defined theory certain
restrictions must be imposed on the lattice. Growth-induced particle creation
is studied in a two-dimensional example. The results suggest that local mode
birth of this sort injects too much energy into the vacuum to be a viable model
of cosmological mode birth.Comment: 28 pages, 2 figures; v.2: added comments on defining energy, and
reference
Perfect mirrors and the self-accelerating box paradox
We consider the question raised by Unruh and Wald of whether mirrored boxes
can self-accelerate in flat spacetime (the ``self-accelerating box paradox'').
From the point of view of the box, which perceives the acceleration as an
impressed gravitational field, this is equivalent to asking whether the box can
be supported by the buoyant force arising from its immersion in a perceived
bath of thermal (Unruh) radiation. The perfect mirrors we study are of the type
that rely on light internal degrees of freedom which adjust to and reflect
impinging radiation. We suggest that a minimum of one internal mirror degree of
freedom is required for each bulk field degree of freedom reflected. A short
calculation then shows that such mirrors necessarily absorb enough heat from
the thermal bath that their increased mass prevents them from floating on the
thermal radiation. For this type of mirror the paradox is therefore resolved.
We also observe that this failure of boxes to ``float'' invalidates one of the
assumptions going into the Unruh-Wald analysis of entropy balances involving
boxes lowered adiabatically toward black holes. Nevertheless, their broad
argument can be maintained until the box reaches a new regime in which
box-antibox pairs dominate over massless fields as contributions to thermal
radiation.Comment: 11 pages, Revtex4, changes made in response to referee and to enhance
clarity, discussion of massive fields correcte
On the Status of Highly Entropic Objects
It has been proposed that the entropy of any object must satisfy fundamental
(holographic or Bekenstein) bounds set by the object's size and perhaps its
energy. However, most discussions of these bounds have ignored the possibility
that objects violating the putative bounds could themselves become important
components of Hawking radiation. We show that this possibility cannot a priori
be neglected in existing derivations of the bounds. Thus this effect could
potentially invalidate these derivations; but it might also lead to
observational evidence for the bounds themselves.Comment: 6 pages, RevTex, a few editorial change
Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
We consider a general, classical theory of gravity with arbitrary matter
fields in dimensions, arising from a diffeomorphism invariant Lagrangian,
\bL. We first show that \bL always can be written in a ``manifestly
covariant" form. We then show that the symplectic potential current
-form, , and the symplectic current -form, \om, for the
theory always can be globally defined in a covariant manner. Associated with
any infinitesimal diffeomorphism is a Noether current -form, \bJ, and
corresponding Noether charge -form, \bQ. We derive a general
``decomposition formula" for \bQ. Using this formula for the Noether charge,
we prove that the first law of black hole mechanics holds for arbitrary
perturbations of a stationary black hole. (For higher derivative theories,
previous arguments had established this law only for stationary perturbations.)
Finally, we propose a local, geometrical prescription for the entropy,
, of a dynamical black hole. This prescription agrees with the Noether
charge formula for stationary black holes and their perturbations, and is
independent of all ambiguities associated with the choices of \bL, , and
\bQ. However, the issue of whether this dynamical entropy in general obeys a
``second law" of black hole mechanics remains open. In an appendix, we apply
some of our results to theories with a nondynamical metric and also briefly
develop the theory of stress-energy pseudotensors.Comment: 30 pages, LaTe
Lodged in the throat: Internal infinities and AdS/CFT
In the context of AdS3/CFT2, we address spacetimes with a certain sort of
internal infinity as typified by the extreme BTZ black hole. The internal
infinity is a null circle lying at the end of the black hole's infinite throat.
We argue that such spacetimes may be described by a product CFT of the form
CFT-L * CFT-R, where CFT-R is associated with the asymptotically AdS boundary
while CFT-L is associated with the null circle. Our particular calculations
analyze the CFT dual of the extreme BTZ black hole in a linear toy model of
AdS3/CFT2. Since the BTZ black hole is a quotient of AdS3, the dual CFT state
is a corresponding quotient of the CFT vacuum state. This state turns out to
live in the aforementioned product CFT. We discuss this result in the context
of general issues of AdS/CFT duality and entanglement entropy.Comment: 11 pages, 2 figures; v2 - some typos corrected, minor revision
On the Origin of the Outgoing Black Hole Modes
The question of how to account for the outgoing black hole modes without
drawing upon a transplanckian reservoir at the horizon is addressed. It is
argued that the outgoing modes must arise via conversion from ingoing modes. It
is further argued that the back-reaction must be included to avoid the
conclusion that particle creation cannot occur in a strictly stationary
background. The process of ``mode conversion" is known in plasma physics by
this name and in condensed matter physics as ``Andreev reflection" or ``branch
conversion". It is illustrated here in a linear Lorentz non-invariant model
introduced by Unruh. The role of interactions and a physical short distance
cutoff is then examined in the sonic black hole formed with Helium-II.Comment: 12 pages, plain latex, 2 figures included using psfig; Analogy to
``Andreev reflection" in superfluid systems noted, references and
acknowledgment added, format changed to shorten tex
Ten Proofs of the Generalized Second Law
Ten attempts to prove the Generalized Second Law of Thermodyanmics (GSL) are
described and critiqued. Each proof provides valuable insights which should be
useful for constructing future, more complete proofs. Rather than merely
summarizing previous research, this review offers new perspectives, and
strategies for overcoming limitations of the existing proofs. A long
introductory section addresses some choices that must be made in any
formulation the GSL: Should one use the Gibbs or the Boltzmann entropy? Should
one use the global or the apparent horizon? Is it necessary to assume any
entropy bounds? If the area has quantum fluctuations, should the GSL apply to
the average area? The definition and implications of the classical,
hydrodynamic, semiclassical and full quantum gravity regimes are also
discussed. A lack of agreement regarding how to define the "quasi-stationary"
regime is addressed by distinguishing it from the "quasi-steady" regime.Comment: 60 pages, 2 figures, 1 table. v2: corrected typos and added a
footnote to match the published versio
The Seven-sphere and its Kac-Moody Algebra
We investigate the seven-sphere as a group-like manifold and its extension to
a Kac-Moody-like algebra. Covariance properties and tensorial composition of
spinors under are defined. The relation to Malcev algebras is
established. The consequences for octonionic projective spaces are examined.
Current algebras are formulated and their anomalies are derived, and shown to
be unique (even regarding numerical coefficients) up to redefinitions of the
currents. Nilpotency of the BRST operator is consistent with one particular
expression in the class of (field-dependent) anomalies. A Sugawara construction
is given.Comment: 22 pages. Macropackages used: phyzzx, epsf. Three epsf figure files
appende
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