12,535 research outputs found
Asymptotic simplicity and static data
The present article considers time symmetric initial data sets for the vacuum
Einstein field equations which in a neighbourhood of infinity have the same
massless part as that of some static initial data set. It is shown that the
solutions to the regular finite initial value problem at spatial infinity for
this class of initial data sets extend smoothly through the critical sets where
null infinity touches spatial infinity if and only if the initial data sets
coincide with static data in a neighbourhood of infinity. This result
highlights the special role played by static data among the class of initial
data sets for the Einstein field equations whose development gives rise to a
spacetime with a smooth conformal compactification at null infinity.Comment: 25 page
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
Initial boundary value problems for Einstein's field equations and geometric uniqueness
While there exist now formulations of initial boundary value problems for
Einstein's field equations which are well posed and preserve constraints and
gauge conditions, the question of geometric uniqueness remains unresolved. For
two different approaches we discuss how this difficulty arises under general
assumptions. So far it is not known whether it can be overcome without imposing
conditions on the geometry of the boundary. We point out a natural and
important class of initial boundary value problems which may offer
possibilities to arrive at a fully covariant formulation.Comment: 19 page
Local twistors and the conformal field equations
This note establishes the connection between Friedrich's conformal field
equations and the conformally invariant formalism of local twistors.Comment: LaTeX2e Minor corrections of misprints et
Rotational and rotationless states of weakly-bound molecules
By making use of the quantization rule of Raab and Friedrich [P. Raab and H.
Friedrich, Phys. Rev. A 78, 022707 (2008)], we derive simple and accurate
formulae for the number of rotational states supported by a weakly-bound
vibrational level of a diatomic molecule and the rotational constants of any
such levels up to the threshold, and provide a criterion for determining
whether a given weakly-bound vibrational level is rotationless. The results
depend solely on the long-range part of the molecular potential and are
applicable to halo molecules.Comment: slightly corrected version, 4 pages, 1 figure, 3 table
A Method for Calculating the Structure of (Singular) Spacetimes in the Large
A formalism and its numerical implementation is presented which allows to
calculate quantities determining the spacetime structure in the large directly.
This is achieved by conformal techniques by which future null infinity
(\Scri{}^+) and future timelike infinity () are mapped to grid points on
the numerical grid. The determination of the causal structure of singularities,
the localization of event horizons, the extraction of radiation, and the
avoidance of unphysical reflections at the outer boundary of the grid, are
demonstrated with calculations of spherically symmetric models with a scalar
field as matter and radiation model.Comment: 29 pages, AGG2
An optical linewidth study of a chromoprotein-C-phycocyanin in a low-temperature glass
The temperature dependence of spectral holes burnt into a phycocyanin-doped ethylene glycol/water glass is investigated in the temperature range between 1.5 and 15 K. The data are well described by a power law with an exponent of 1.16 ± 0.1. Chromoproteins thus behave very much the same as glasses doped with small impurity molecules
Numerical treatment of the hyperboloidal initial value problem for the vacuum Einstein equations. I. The conformal field equations
This is the first in a series of articles on the numerical solution of
Friedrich's conformal field equations for Einstein's theory of gravity. We will
discuss in this paper why one should be interested in applying the conformal
method to physical problems and why there is good hope that this might even be
a good idea from the numerical point of view. We describe in detail the
derivation of the conformal field equations in the spinor formalism which we
use for the implementation of the equations, and present all the equations as a
reference for future work. Finally, we discuss the implications of the
assumptions of a continuous symmetry.Comment: 19 pages, LaTeX2
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