389 research outputs found
Emergence of thin shell structure during collapse in isotropic coordinates
Numerical studies of gravitational collapse in isotropic coordinates have
recently shown an interesting connection between the gravitational Lagrangian
and black hole thermodynamics. A study of the actual spacetime was not the main
focus of this work and in particular, the rich and interesting structure of the
interior has not been investigated in much detail and remains largely unknown.
We elucidate its features by performing a numerical study of the spacetime in
isotropic coordinates during gravitational collapse of a massless scalar field.
The most salient feature to emerge is the formation of a thin shell of matter
just inside the apparent horizon. The energy density and Ricci scalar peak at
the shell and there is a jump discontinuity in the extrinsic curvature across
the apparent horizon, the hallmark that a thin shell is present in its
vicinity. At late stages of the collapse, the spacetime consists of two vacuum
regions separated by the thin shell. The interior is described by an
interesting collapsing isotropic universe. It tends towards a vacuum (never
reaches a perfect vacuum) and there is a slight inhomogeneity in the interior
that plays a crucial role in the collapse process as the areal radius tends to
zero. The spacetime evolves towards a curvature (physical) singularity in the
interior, both a Weyl and Ricci singularity. In the exterior, our numerical
results match closely the analytical form of the Schwarzschild metric in
isotropic coordinates, providing a strong test of our numerical code.Comment: 24 pages, 10 figures. version to appear in Phys. Rev.
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
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
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 Randall-Sundrum Models
The finite temperature Casimir effect for a scalar field in the bulk region
of the two Randall-Sundrum models, RSI and RSII, is studied. We calculate the
Casimir energy and the Casimir force for two parallel plates with separation
on the visible brane in the RSI model. High-temperature and low-temperature
cases are covered. Attractiveness versus repulsiveness of the temperature
correction to the force is discussed in the typical special cases of
Dirichlet-Dirichlet, Neumann-Neumann, and Dirichlet-Neumann boundary conditions
at low temperature. The Abel-Plana summation formula is made use of, as this
turns out to be most convenient. Some comments are made on the related
contemporary literature.Comment: 33 pages latex, 2 figures. Some changes in the discussion. To appear
in New J. Phy
Spherically Symmetric Braneworld Solutions with R_{4} term in the Bulk
An analysis of a spherically symmetric braneworld configuration is performed
when the intrinsic curvature scalar is included in the bulk action; the
vanishing of the electric part of the Weyl tensor is used as the boundary
condition for the embedding of the brane in the bulk. All the solutions outside
a static localized matter distribution are found; some of them are of the
Schwarzschild-(A)dS_{4} form. Two modified Oppenheimer-Volkoff interior
solutions are also found; one is matched to a Schwarzschild-(A)dS_{4} exterior,
while the other does not. A non-universal gravitational constant arises,
depending on the density of the considered object; however, the conventional
limits of the Newton's constant are recovered. An upper bound of the order of
TeV for the energy string scale is extracted from the known solar system
measurements (experiments). On the contrary, in usual brane dynamics, this
string scale is calculated to be larger than TeV.Comment: 23 pages, 1 figure, one minor chang
Kaluza-Klein Pistons with non-Commutative Extra Dimensions
We calculate the scalar Casimir energy and Casimir force for a
Kaluza-Klein piston setup in which the extra dimensional space contains a
non-commutative 2-sphere, . The cases to be studied are and respectively as extra dimensional spaces, with the
dimensional commutative torus. The validity of the results and the
regularization that the piston setup offers are examined in both cases. Finally
we examine the 1-loop corrected Casimir energy for one piston chamber, due to
the self interacting scalar field in the non-commutative geometry. The
computation is done within some approximations. We compare this case for the
same calculation done in Minkowski spacetime . A discussion on the
stabilization of the extra dimensional space within the piston setup follows at
the end of the article.Comment: 22 page
Comment on the sign of the Casimir force
I show that reflection positivity implies that the force between any mirror
pair of charge-conjugate probes of the quantum vacuum is attractive. This
generalizes a recent theorem of Kenneth and Klich to interacting quantum
fields, to arbitrary semiclassical bodies, and to quantized probes with
non-overlapping wavefunctions. I also prove that the torques on
charge-conjugate probes tend always to rotate them into a mirror-symmetric
position.Comment: 13 pages, 1 figure, Latex file. Several points clarified and
expanded, two references added
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