1,779 research outputs found
Metric-Torsional Conformal Gravity
When in general geometric backgrounds the metric is accompanied by torsion,
the metric conformal properties should correspondingly be followed by analogous
torsional conformal properties; however a combined metric torsional conformal
structure has never been found which provides a curvature that is both
containing metric-torsional degree of freedom and conformally invariant: in
this paper we construct such a metric-torsional conformal curvature. We proceed
by building the most general action, then deriving the most general system of
field equations; we check their consistency by showing that both conservation
laws and trace condition are verified. Final considerations and comments are
outlined.Comment: 6 page
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.
Generating Einstein gravity, cosmological constant and Higgs mass from restricted Weyl invariance
Recently, it has been pointed out that dimensionless actions in four
dimensional curved spacetime possess a symmetry which goes beyond scale
invariance but is smaller than full Weyl invariance. This symmetry was dubbed
{\it restricted Weyl invariance}. We show that starting with a restricted Weyl
invariant action that includes a Higgs sector with no explicit mass, one can
generate the Einstein-Hilbert action with cosmological constant and a Higgs
mass. The model also contains an extra massless scalar field which couples to
the Higgs field (and gravity). If the coupling of this extra scalar field to
the Higgs field is negligibly small, this fixes the coefficient of the
nonminimal coupling between the Higgs field and gravity. Besides the
Higgs sector, all the other fields of the standard model can be incorporated
into the original restricted Weyl invariant action.Comment: 7 pages, no figure
Three dimensional Casimir piston for massive scalar fields
We consider Casimir force acting on a three dimensional rectangular piston
due to a massive scalar field subject to periodic, Dirichlet and Neumann
boundary conditions. Exponential cut-off method is used to derive the Casimir
energy in the interior region and the exterior region separated by the piston.
It is shown that the divergent term of the Casimir force acting on the piston
due to the interior region cancels with that due to the exterior region, thus
render a finite well-defined Casimir force acting on the piston. Explicit
expressions for the total Casimir force acting on the piston is derived, which
show that the Casimir force is always attractive for all the different boundary
conditions considered. As a function of a -- the distance from the piston to
the opposite wall, it is found that the magnitude of the Casimir force behaves
like when and decays exponentially when .
Moreover, the magnitude of the Casimir force is always a decreasing function of
a. On the other hand, passing from massless to massive, we find that the effect
of the mass is insignificant when a is small, but the magnitude of the force is
decreased for large a in the massive case.Comment: 22 pages, 8 figure
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
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