434 research outputs found
Causal Structure of Vacuum Solutions to Conformal(Weyl) Gravity
Using Penrose diagrams the causal structure of the static spherically
symmetric vacuum solution to conformal (Weyl) gravity is investigated. A
striking aspect of the solution is an unexpected physical singularity at
caused by a linear term in the metric. We explain how to calculate the
deflection of light in coordinates where the metric is manifestly conformal to
flat i.e. in coordinates where light moves in straight lines.Comment: 18 pages, 2 figures, title and abstract changed, contents essentially
unaltered accepted for publication in General Relativity and Gravitatio
Casimir forces in Bose-Einstein condensates: finite size effects in three-dimensional rectangular cavities
The Casimir force due to {\it thermal} fluctuations (or pseudo-Casimir force)
was previously calculated for the perfect Bose gas in the slab geometry for
various boundary conditions. The Casimir pressure due to {\it quantum}
fluctuations in a weakly-interacting dilute Bose-Einstein condensate (BEC)
confined to a parallel plate geometry was recently calculated for Dirichlet
boundary conditions. In this paper we calculate the Casimir energy and pressure
due to quantum fluctuations in a zero-temperature homogeneous
weakly-interacting dilute BEC confined to a parallel plate geometry with
periodic boundary conditions and include higher-order corrections which we
refer to as Bogoliubov corrections. The leading order term is identified as the
Casimir energy of a massless scalar field moving with wave velocity equal to
the speed of sound in the BEC. We then obtain the leading order Casimir
pressure in a general three-dimensional rectangular cavity of arbitrary lengths
and obtain the finite-size correction to the parallel plate scenario.Comment: 12 pages; no figures; v.2: version accepted for publication in JSTAT
v.3: references adde
The Bright Side of Dark Matter
We show that it is not possible in the absence of dark matter to construct a
four-dimensional metric that explains galactic observations. In particular, by
working with an effective potential it is shown that a metric which is
constructed to fit flat rotation curves in spiral galaxies leads to the wrong
sign for the bending of light i.e. repulsion instead of attraction. Hence,
without dark matter the motion of particles on galactic scales cannot be
explained in terms of geodesic motion on a four- dimensional metric. This
reveals a new bright side to dark matter: it is indispensable if we wish to
retain the cherished equivalence principle.Comment: 7 pages, latex, no figures. Received an honorable mention in the 1999
Gravity research Foundation Essay Competition. Submitted to Phys. Rev. Let
Casimir Energy of a BEC: From Moderate Interactions to the Ideal Gas
Considering the Casimir effect due to phononic excitations of a weakly
interacting dilute {BEC}, we derive a re-normalized expression for the zero
temperature Casimir energy of a {BEC} confined to a parallel
plate geometry with periodic boundary conditions. Our expression is formally
equivalent to the free energy of a bosonic field at finite temperature, with a
nontrivial density of modes that we compute analytically. As a function of the
interaction strength, smoothly describes the transition from
the weakly interacting Bogoliubov regime to the non-interacting ideal {BEC}.
For the weakly interacting case, reduces to leading order to
the Casimir energy due to zero-point fluctuations of massless phonon modes. In
the limit of an ideal Bose gas, our result correctly describes the Casimir
energy going to zero.Comment: 12 pages, 3 figures, accepted for publication in JPA. New version
with corrected typos and an additional appendi
Light deflection in Weyl gravity: critical distances for photon paths
The Weyl gravity appears to be a very peculiar theory. The contribution of
the Weyl linear parameter to the effective geodesic potential is opposite for
massive and nonmassive geodesics. However, photon geodesics do not depend on
the unknown conformal factor, unlike massive geodesics. Hence light deflection
offers an interesting test of the Weyl theory.
In order to investigate light deflection in the setting of Weyl gravity, we
first distinguish between a weak field and a strong field approximation.
Indeed, the Weyl gravity does not turn off asymptotically and becomes even
stronger at larger distances.
We then take full advantage of the conformal invariance of the photon
effective potential to provide the key radial distances in Weyl gravity.
According to those, we analyze the weak and strong field regime for light
deflection. We further show some amazing features of the Weyl theory in the
strong regime.Comment: 20 pages, 9 figures (see published version for a better resolution,
or online version at stacks.iop.org/CQG/21/1897
Semi-automated dialogue act classification for situated social agents in games
As a step toward simulating dynamic dialogue between agents and humans in virtual environments, we describe learning a model of social behavior composed of interleaved utterances and physical actions. In our model, utterances are abstracted as {speech act, propositional content, referent} triples. After training a classifier on 100 gameplay logs from The Restaurant Game annotated with dialogue act triples, we have automatically classified utterances in an additional 5,000 logs. A quantitative evaluation of statistical models learned from the gameplay logs demonstrates that semi-automatically classified dialogue acts yield significantly more predictive power than automatically clustered utterances, and serve as a better common currency for modeling interleaved actions and utterances
Implications of Cosmic Repulsion for Gravitational Theory
In this paper we present a general, model independent analysis of a recently
detected apparent cosmic repulsion, and discuss its potential implications for
gravitational theory. In particular, we show that a negatively spatially curved
universe acts like a diverging refractive medium, to thus naturally cause
galaxies to accelerate away from each other. Additionally, we show that it is
possible for a cosmic acceleration to only be temporary, with some accelerating
universes actually being able to subsequently recontract.Comment: RevTeX, 13 page
Casimir force on interacting Bose-Einstein condensate
We have presented an analytic theory for the Casimir force on a Bose-Einstein
condensate (BEC) which is confined between two parallel plates. We have
considered Dirichlet boundary conditions for the condensate wave function as
well as for the phonon field. We have shown that, the condensate wave function
(which obeys the Gross-Pitaevskii equation) is responsible for the mean field
part of Casimir force, which usually dominates over the quantum (fluctuations)
part of the Casimir force.Comment: Accepted in Journal of Physics B: Atomic, Molecular and Optical
Physic
Multidimensional cut-off technique, odd-dimensional Epstein zeta functions and Casimir energy of massless scalar fields
Quantum fluctuations of massless scalar fields represented by quantum
fluctuations of the quasiparticle vacuum in a zero-temperature dilute
Bose-Einstein condensate may well provide the first experimental arena for
measuring the Casimir force of a field other than the electromagnetic field.
This would constitute a real Casimir force measurement - due to quantum
fluctuations - in contrast to thermal fluctuation effects. We develop a
multidimensional cut-off technique for calculating the Casimir energy of
massless scalar fields in -dimensional rectangular spaces with large
dimensions and dimensions of length and generalize the technique to
arbitrary lengths. We explicitly evaluate the multidimensional remainder and
express it in a form that converges exponentially fast. Together with the
compact analytical formulas we derive, the numerical results are exact and easy
to obtain. Most importantly, we show that the division between analytical and
remainder is not arbitrary but has a natural physical interpretation. The
analytical part can be viewed as the sum of individual parallel plate energies
and the remainder as an interaction energy. In a separate procedure, via
results from number theory, we express some odd-dimensional homogeneous Epstein
zeta functions as products of one-dimensional sums plus a tiny remainder and
calculate from them the Casimir energy via zeta function regularization.Comment: 42 pages, 3 figures. v.2: typos corrected to match published versio
A simple theorem to generate exact black hole solutions
Under certain conditions imposed on the energy-momentum tensor, a theorem
that characterizes a two-parameter family of static and spherically symmetric
solutions to Einstein's field equations (black holes), is proved. A discussion
on the asymptotics, regularity, and the energy conditions is provided. Examples
that include the best known exact solutions within these symmetries are
considered. A trivial extension of the theorem includes the cosmological
constant {\it ab-initio}, providing then a three-parameter family of solutions.Comment: 14 pages; RevTex; no figures; typos corrected; references adde
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