629 research outputs found
On Casimir Pistons
In this paper we study the Casimir force for a piston configuration in
with one dimension being slightly curved and the other two infinite. We work
for two different cases with this setup. In the first, the piston is "free to
move" along a transverse dimension to the curved one and in the other case the
piston "moves" along the curved one. We find that the Casimir force has
opposite signs in the two cases. We also use a semi-analytic method to study
the Casimir energy and force. In addition we discuss some topics for the
aforementioned piston configuration in and for possible modifications
from extra dimensional manifolds.Comment: 20 pages, To be published in MPL
The perfect magnetic conductor (PMC) Casimir piston in d+1 dimensions
Perfect magnetic conductor (PMC) boundary conditions are dual to the more
familiar perfect electric conductor (PEC) conditions and can be viewed as the
electromagnetic analog of the boundary conditions in the bag model for hadrons
in QCD. Recent advances and requirements in communication technologies have
attracted great interest in PMC's and Casimir experiments involving structures
that approximate PMC's may be carried out in the not too distant future. In
this paper, we make a study of the zero-temperature PMC Casimir piston in
dimensions. The PMC Casimir energy is explicitly evaluated by summing over
-dimensional Dirichlet energies where p ranges from 2 to inclusively.
We derive two exact -dimensional expressions for the Casimir force on the
piston and find that the force is negative (attractive) in all dimensions. Both
expressions are applied to the case of 2+1 and 3+1 dimensions. A spin-off from
our work is a contribution to the PEC literature: we obtain a useful
alternative expression for the PEC Casimir piston in 3+1 dimensions and also
evaluate the Casimir force per unit area on an infinite strip, a geometry of
experimental interest.Comment: 18 pages, 1 figure, to appear in Phys. Rev.
Spontaneous breaking of conformal invariance in theories of conformally coupled matter and Weyl gravity
We study the theory of Weyl conformal gravity with matter degrees of freedom
in a conformally invariant interaction. Specifically, we consider a triplet of
scalar fields and SO(3) non-abelian gauge fields, i.e. the Georgi-Glashow model
conformally coupled to Weyl gravity. We show that the equations of motion admit
solutions spontaneously breaking the conformal symmetry and the gauge symmetry,
providing a mechanism for supplying a scale in the theory. The vacuum solution
corresponds to anti-de-Sitter space-time, while localized soliton solutions
correspond to magnetic monopoles in asymptotically anti-de-Sitter space-time.
The resulting effective action gives rise to Einstein gravity and the residual
U(1) gauge theory. This mechanism strengthens the reasons for considering
conformally invariant matter-gravity theory, which has shown promising
indications concerning the problem of missing matter in galactic rotation
curves.Comment: 20 pages, 1 figure, revised and added reference
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
Extremal black holes, gravitational entropy and nonstationary metric fields
We show that extremal black holes have zero entropy by pointing out a simple
fact: they are time-independent throughout the spacetime and correspond to a
single classical microstate. We show that non-extremal black holes, including
the Schwarzschild black hole, contain a region hidden behind the event horizon
where all their Killing vectors are spacelike. This region is nonstationary and
the time labels a continuous set of classical microstates, the phase space
, where is a three-metric induced on a
spacelike hypersurface and is its momentum conjugate. We
determine explicitly the phase space in the interior region of the
Schwarzschild black hole. We identify its entropy as a measure of an outside
observer's ignorance of the classical microstates in the interior since the
parameter which labels the states lies anywhere between 0 and 2M. We
provide numerical evidence from recent simulations of gravitational collapse in
isotropic coordinates that the entropy of the Schwarzschild black hole stems
from the region inside and near the event horizon where the metric fields are
nonstationary; the rest of the spacetime, which is static, makes no
contribution. Extremal black holes have an event horizon but in contrast to
non-extremal black holes, their extended spacetimes do not possess a bifurcate
Killing horizon. This is consistent with the fact that extremal black holes are
time-independent and therefore have no distinct time-reverse.Comment: 12 pages, 2 figures. To appear in Class. and Quant. Gravity. Based on
an essay selected for honorable mention in the 2010 gravity research
foundation essay competitio
Cancellation of nonrenormalizable hypersurface divergences and the d-dimensional Casimir piston
Using a multidimensional cut-off technique, we obtain expressions for the
cut-off dependent part of the vacuum energy for parallelepiped geometries in
any spatial dimension d. The cut-off part yields nonrenormalizable hypersurface
divergences and we show explicitly that they cancel in the Casimir piston
scenario in all dimensions. We obtain two different expressions for the
d-dimensional Casimir force on the piston where one expression is more
convenient to use when the plate separation a is large and the other when a is
small (a useful duality). The Casimir force on the piston is found
to be attractive (negative) for any dimension d. We apply the d-dimensional
formulas (both expressions) to the two and three-dimensional Casimir piston
with Neumann boundary conditions. The 3D Neumann results are in numerical
agreement with those recently derived in arXiv:0705.0139 using an optical path
technique providing an independent confirmation of our multidimensional
approach. We limit our study to massless scalar fields.Comment: 29 pages; 3 figures; references added; to appear in JHE
Casimir piston for massless scalar fields in three dimensions
We study the Casimir piston for massless scalar fields obeying Dirichlet
boundary conditions in a three dimensional cavity with sides of arbitrary
lengths and where is the plate separation. We obtain an exact
expression for the Casimir force on the piston valid for any values of the
three lengths. As in the electromagnetic case with perfect conductor
conditions, we find that the Casimir force is negative (attractive) regardless
of the values of , and . Though cases exist where the interior
contributes a positive (repulsive) Casimir force, the total Casimir force on
the piston is negative when the exterior contribution is included. We also
obtain an alternative expression for the Casimir force that is useful
computationally when the plate separation is large.Comment: 19 pages,3 figures; references updated and typos fixed to match
published versio
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
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