A rigorous formulation of the cosmological Newtonian limit without averaging

We prove the existence of a large class of one-parameter families of cosmological solutions to the Einstein-Euler equations that have a Newtonian limit. This class includes solutions that represent a finite, but otherwise arbitrary, number of compact fluid bodies. These solutions provide exact cosmological models that admit Newtonian limits but, are not, either implicitly or explicitly, averaged

Post-Newtonian extension of the Newton-Cartan theory

The theory obtained as a singular limit of General Relativity, if the reciprocal velocity of light is assumed to tend to zero, is known to be not exactly the Newton-Cartan theory, but a slight extension of this theory. It involves not only a Coriolis force field, which is natural in this theory (although not original Newtonian), but also a scalar field which governs the relation between Newtons time and relativistic proper time. Both fields are or can be reduced to harmonic functions, and must therefore be constants, if suitable global conditions are imposed. We assume this reduction of Newton-Cartan to Newton`s original theory as starting point and ask for a consistent post-Newtonian extension and for possible differences to usual post-Minkowskian approximation methods, as developed, for example, by Chandrasekhar. It is shown, that both post-Newtonian frameworks are formally equivalent, as far as the field equations and the equations of motion for a hydrodynamical fluid are concerned.Comment: 13 pages, LaTex, to appear in Class. Quantum Gra

Theory of the "honeycomb chain-channel" reconstruction of Si(111)3x1

First-principles electronic-structure methods are used to study a structural model for Ag/Si(111)3x1 recently proposed on the basis of transmission electron diffraction data. The fully relaxed geometry for this model is far more energetically favorable than any previously proposed, partly due to the unusual formation of a Si double bond in the surface layer. The calculated electronic properties of this model are in complete agreement with data from angle-resolved photoemission and scanning tunneling microscopy.Comment: 4 pages, 4 figures, submitted to Phys. Rev. Lett (the ugly postscript error on page 4 has now been repaired

The multiferroic phases of (Eu:Y)MnO3

We report on structural, magnetic, dielectric, and thermodynamic properties of (Eu:Y)MnO3 for Y doping levels 0 <= x < 1. This system resembles the multiferroic perovskite manganites RMnO3 (with R= Gd, Dy, Tb) but without the interference of magnetic contributions of the 4f-ions. In addition, it offers the possibility to continuously tune the influence of the A-site ionic radii. For small concentrations x <= 0.1 we find a canted antiferromagnetic and paraelectric groundstate. For higher concentrations x <= 0.3 ferroelectric polarization coexists with the features of a long wavelength incommensurate spiral magnetic phase analogous to the observations in TbMnO3. In the intermediate concentration range around x = 0.2 a multiferroic scenario is realized combining weak ferroelectricity and weak ferromagnetism, presumably due to a canted spiral magnetic structure.Comment: 8 pages, 8 figure

The Newtonian Limit for Asymptotically Flat Solutions of the Vlasov-Einstein System

It is shown that there exist families of asymptotically flat solutions of the Einstein equations coupled to the Vlasov equation describing a collisionless gas which have a Newtonian limit. These are sufficiently general to confirm that for this matter model as many families of this type exist as would be expected on the basis of physical intuition. A central role in the proof is played by energy estimates in unweighted Sobolev spaces for a wave equation satisfied by the second fundamental form of a maximal foliation.Comment: 24 pages, plain TE

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 $\lambda$, which can be thought of as $1/c^2$, where $c$ is the speed of light. By construction, frame theory is equivalent to general relativity for $\lambda >0$, and reduces to Newtonian gravity for $\lambda =0$. Moreover, by setting \ep=\sqrt{\lambda}, frame theory provides a framework to study the Newtonian limit \ep \searrow 0 (i.e. $c\to \infty$). 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

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 $c$ is the speed of light, and $v_T$ 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

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 $v_T$ is a characteristic velocity associated with the fluid and $c$ 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

The Relation between Ion Temperature Anisotropy and Formation of Slow Shocks in Collisionless Magnetic Reconnection

We perform a two-dimensional simulation by using an electromagnetic hybrid code to study the formation of slow-mode shocks in collisionless magnetic reconnection in low beta plasmas, and we focus on the relation between the formation of slow shocks and the ion temperature anisotropy enhanced at the shock downstream region. It is known that as magnetic reconnection develops, the parallel temperature along the magnetic field becomes large in association with the anisotropic PSBL (plasma sheet boundary layer) ion beams, and this temperature anisotropy has a tendency to suppress the formation of slow shocks. Based on our simulation result, we found that the slow shock formation is suppressed due to the large temperature anisotropy near the X-type region, but the ion temperature anisotropy relaxes with increasing the distance from the magnetic neutral point. As a result, two pairs of current structures, which are the strong evidence of dissipation of magnetic field in slow shocks, are formed at the distance x > 115 ion inertial lengths from the neutral point.Comment: 28 pages, 8 figures, accepted for publication in JG

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