9,654 research outputs found
General Relativistic Scalar Field Models in the Large
For a class of scalar fields including the massless Klein-Gordon field the
general relativistic hyperboloidal initial value problems are equivalent in a
certain sense. By using this equivalence and conformal techniques it is proven
that the hyperboloidal initial value problem for those scalar fields has an
unique solution which is weakly asymptotically flat. For data sufficiently
close to data for flat spacetime there exist a smooth future null infinity and
a regular future timelike infinity.Comment: 22 pages, latex, AGG 1
First-order symmetrizable hyperbolic formulations of Einstein's equations including lapse and shift as dynamical fields
First-order hyperbolic systems are promising as a basis for numerical
integration of Einstein's equations. In previous work, the lapse and shift have
typically not been considered part of the hyperbolic system and have been
prescribed independently. This can be expensive computationally, especially if
the prescription involves solving elliptic equations. Therefore, including the
lapse and shift in the hyperbolic system could be advantageous for numerical
work. In this paper, two first-order symmetrizable hyperbolic systems are
presented that include the lapse and shift as dynamical fields and have only
physical characteristic speeds.Comment: 11 page
Controlled nanochannel lattice formation utilizing prepatterned substrates
Solid substrates can be endued with self-organized regular stripe patterns of
nanoscopic lengthscale by Langmuir-Blodgett transfer of organic monolayers.
Here we consider the effect of periodically prepatterned substrates on this
process of pattern formation. It leads to a time periodic forcing of the
oscillatory behavior at the meniscus. Utilizing higher order synchronization
with this forcing, complex periodic patterns of predefined wavelength can be
created. The dependence of the synchronization on the amplitude and the
wavelength of the wetting contrast is investigated in one and two spatial
dimensions and the resulting patterns are discussed. Furthermore, the effect of
prepatterned substrates on the pattern selection process is investigated
Initial states and infrared physics in locally de Sitter spacetime
The long wavelength physics in a de Sitter region depends on the initial
quantum state. While such long wavelength physics is under control for massive
fields near the Hartle-Hawking vacuum state, such initial states make unnatural
assumptions about initial data outside the region of causal contact of a local
observer. We argue that a reasonable approximation to a maximum entropy state,
one that makes minimal assumptions outside an observer's horizon volume, is one
where a cutoff is placed on a surface bounded by timelike geodesics, just
outside the horizon. For sufficiently early times, such a cutoff induces
secular logarithmic divergences with the expansion of the region. For massive
fields, these effects sum to finite corrections at sufficiently late times. The
difference between the cutoff correlators and Hartle-Hawking correlators
provides a measure of the theoretical uncertainty due to lack of knowledge of
the initial state in causally disconnected regions. These differences are
negligible for primordial inflation, but can become significant during epochs
with very long-lived de Sitter regions, such as we may be entering now.Comment: 19 pages, 4 figures, references adde
Influence of the Particles Creation on the Flat and Negative Curved FLRW Universes
We present a dynamical analysis of the (classical) spatially flat and
negative curved Friedmann-Lameitre-Robertson-Walker (FLRW) universes evolving,
(by assumption) close to the thermodynamic equilibrium, in presence of a
particles creation process, described by means of a realiable phenomenological
approach, based on the application to the comoving volume (i. e. spatial volume
of unit comoving coordinates) of the theory for open thermodynamic systems. In
particular we show how, since the particles creation phenomenon induces a
negative pressure term, then the choice of a well-grounded ansatz for the time
variation of the particles number, leads to a deep modification of the very
early standard FLRW dynamics. More precisely for the considered FLRW models, we
find (in addition to the limiting case of their standard behaviours) solutions
corresponding to an early universe characterized respectively by an "eternal"
inflationary-like birth and a spatial curvature dominated singularity. In both
these cases the so-called horizon problem finds a natural solution.Comment: 14 pages, no figures, appeared in Class. Quantum Grav., 18, 193, 200
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