470 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
The Stefan-Boltzmann law in a small box and the pressure deficit in hot SU(N) lattice gauge theory
The blackbody radiation in a box L^3 with periodic boundary conditions in
thermal equilibrium at a temperature T is affected by finite-size effects.
These bring about modifications of the thermodynamic functions which can be
expressed in a closed form in terms of the dimensionless parameter LT. For
instance, when LT~4 - corresponding to the value where the most reliable SU(N)
gauge lattice simulations have been performed above the deconfining temperature
T_c - the deviation of the free energy density from its thermodynamic limit is
about 5%. This may account for almost half of the pressure deficit observed in
lattice simulations at T~ 4 T_c.Comment: 9 pages, 2 figures v2:a side remark on the final result and
references adde
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
Finite Temperature Casimir Effect and Dispersion in the Presence of Compactified Extra Dimensions
Finite temperature Casimir theory of the Dirichlet scalar field is developed,
assuming that there is a conventional Casimir setup in physical space with two
infinitely large plates separated by a gap R and in addition an arbitrary
number q of extra compacified dimensions. As a generalization of earlier
theory, we assume in the first part of the paper that there is a scalar
'refractive index' N filling the whole of the physical space region. After
presenting general expressions for free energy and Casimir forces we focus on
the low temperature case, as this is of main physical interest both for force
measurements and also for issues related to entropy and the Nernst theorem.
Thereafter, in the second part we analyze dispersive properties, assuming for
simplicity q=1, by taking into account dispersion associated with the first
Matsubara frequency only. The medium-induced contribution to the free energy,
and pressure, is calculated at low temperatures.Comment: 25 pages, one figure. Minor changes in the discussion. Version to
appear in Physica Script
Casimir interaction: pistons and cavity
The energy of a perfectly conducting rectangular cavity is studied by making
use of pistons' interactions. The exact solution for a 3D perfectly conducting
piston with an arbitrary cross section is being discussed.Comment: 10 pages, 2 figures, latex2
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
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
Finite temperature Casimir pistons for electromagnetic field with mixed boundary conditions and its classical limit
In this paper, the finite temperature Casimir force acting on a
two-dimensional Casimir piston due to electromagnetic field is computed. It was
found that if mixed boundary conditions are assumed on the piston and its
opposite wall, then the Casimir force always tends to restore the piston
towards the equilibrium position, regardless of the boundary conditions assumed
on the walls transverse to the piston. In contrary, if pure boundary conditions
are assumed on the piston and the opposite wall, then the Casimir force always
tend to pull the piston towards the closer wall and away from the equilibrium
position. The nature of the force is not affected by temperature. However, in
the high temperature regime, the magnitude of the Casimir force grows linearly
with respect to temperature. This shows that the Casimir effect has a classical
limit as has been observed in other literatures.Comment: 14 pages, 3 figures, accepted by Journal of Physics
Finite temperature Casimir effect in piston geometry and its classical limit
We consider the Casimir force acting on a -dimensional rectangular piston
due to massless scalar field with periodic, Dirichlet and Neumann boundary
conditions and electromagnetic field with perfect electric conductor and
perfect magnetic conductor boundary conditions. It is verified analytically
that at any temperature, the Casimir force acting on the piston is always an
attractive force pulling the piston towards the interior region, and the
magnitude of the force gets larger as the separation gets smaller. Explicit
exact expressions for the Casimir force for small and large plate separations
and for low and high temperatures are computed. The limits of the Casimir force
acting on the piston when some pairs of transversal plates are large are also
derived. An interesting result regarding the influence of temperature is that
in contrast to the conventional result that the leading term of the Casimir
force acting on a wall of a rectangular cavity at high temperature is the
Stefan--Boltzmann (or black body radiation) term which is of order ,
it is found that the contributions of this term from the interior and exterior
regions cancel with each other in the case of piston. The high temperature
leading order term of the Casimir force acting on the piston is of order ,
which shows that the Casimir force has a nontrivial classical
limit
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