576 research outputs found
Existence of axially symmetric static solutions of the Einstein-Vlasov system
We prove the existence of static, asymptotically flat non-vacuum spacetimes
with axial symmetry where the matter is modeled as a collisionless gas. The
axially symmetric solutions of the resulting Einstein-Vlasov system are
obtained via the implicit function theorem by perturbing off a suitable
spherically symmetric steady state of the Vlasov-Poisson system.Comment: 32 page
Existence of families of spacetimes with a Newtonian limit
J\"urgen Ehlers developed \emph{frame theory} to better understand the
relationship between general relativity and Newtonian gravity. Frame theory
contains a parameter , which can be thought of as , where
is the speed of light. By construction, frame theory is equivalent to general
relativity for , and reduces to Newtonian gravity for .
Moreover, by setting \ep=\sqrt{\lambda}, frame theory provides a framework to
study the Newtonian limit \ep \searrow 0 (i.e. ). A number of
ideas relating to frame theory that were introduced by J\"urgen have
subsequently found important applications to the rigorous study of both the
Newtonian limit and post-Newtonian expansions. In this article, we review frame
theory and discuss, in a non-technical fashion, some of the rigorous results on
the Newtonian limit and post-Newtonian expansions that have followed from
J\"urgen's work
Isotope shift calculations for atoms with one valence electron
This work presents a method for the ab initio calculation of isotope shift in
atoms and ions with one valence electron above closed shells. As a zero
approximation we use relativistic Hartree-Fock and then calculate correlation
corrections. The main motivation for developing the method comes from the need
to analyse whether different isotope abundances in early universe can
contribute to the observed anomalies in quasar absorption spectra. The current
best explanation for these anomalies is the assumption that the fine structure
constant, alpha, was smaller at early epoch. We test the isotope shift method
by comparing the calculated and experimental isotope shift for the alkali and
alkali-like atoms Na, MgII, K, CaII and BaII. The agreement is found to be
good. We then calculate the isotope shift for some astronomically relevant
transitions in SiII and SiIV, MgII, ZnII and GeII.Comment: 11 page
Cosmological post-Newtonian expansions to arbitrary order
We prove the existence of a large class of one parameter families of
solutions to the Einstein-Euler equations that depend on the singular parameter
\ep=v_T/c (0<\ep < \ep_0), where is the speed of light, and is a
typical speed of the gravitating fluid. These solutions are shown to exist on a
common spacetime slab M\cong [0,T)\times \Tbb^3, and converge as \ep
\searrow 0 to a solution of the cosmological Poisson-Euler equations of
Newtonian gravity. Moreover, we establish that these solutions can be expanded
in the parameter \ep to any specified order with expansion coefficients that
satisfy \ep-independent (nonlocal) symmetric hyperbolic equations
Time-Independent Gravitational Fields
This article reviews, from a global point of view, rigorous results on time
independent spacetimes. Throughout attention is confined to isolated bodies at
rest or in uniform rotation in an otherwise empty universe. The discussion
starts from first principles and is, as much as possible, self-contained.Comment: 47 pages, LaTeX, uses Springer cl2emult styl
Post-Newtonian expansions for perfect fluids
We prove the existence of a large class of dynamical solutions to the
Einstein-Euler equations that have a first post-Newtonian expansion. The
results here are based on the elliptic-hyperbolic formulation of the
Einstein-Euler equations used in \cite{Oli06}, which contains a singular
parameter \ep = v_T/c, where is a characteristic velocity associated
with the fluid and is the speed of light. As in \cite{Oli06}, energy
estimates on weighted Sobolev spaces are used to analyze the behavior of
solutions to the Einstein-Euler equations in the limit \ep\searrow 0, and to
demonstrate the validity of the first post-Newtonian expansion as an
approximation
Theorems on existence and global dynamics for the Einstein equations
This article is a guide to theorems on existence and global dynamics of
solutions of the Einstein equations. It draws attention to open questions in
the field. The local-in-time Cauchy problem, which is relatively well
understood, is surveyed. Global results for solutions with various types of
symmetry are discussed. A selection of results from Newtonian theory and
special relativity that offer useful comparisons is presented. Treatments of
global results in the case of small data and results on constructing spacetimes
with prescribed singularity structure or late-time asymptotics are given. A
conjectural picture of the asymptotic behaviour of general cosmological
solutions of the Einstein equations is built up. Some miscellaneous topics
connected with the main theme are collected in a separate section.Comment: Submitted to Living Reviews in Relativity, major update of Living
Rev. Rel. 5 (2002)
Staggering of the Nuclear Charge Radii in a Superfluid Model with Good Particle Number
A simple superfluid model with an effective four body interaction of monopole
pairing type is used to explain the staggering of the charge radii in the
isotope chains. The contribution of deformation and of the particle number
projection are analyzed for the Sn isotopes. Good results are obtained for the
staggering parameters and neutron pairing energies.Comment: RevTex, 19 pages and 4 postscript figures uuencoded and attached. To
appear in Phys. Rev.
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