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

Incompatible Magnetic Order in Multiferroic Hexagonal DyMnO3

Magnetic order of the manganese and rare-earth lattices according to different symmetry representations is observed in multiferroic hexagonal (h-) DyMnO$_3$ by optical second harmonic generation and neutron diffraction. The incompatibility reveals that the 3d-4f coupling in the h-$R$MnO$_3$ system ($R$ = Sc, Y, In, Dy - Lu) is substantially less developed than commonly expected. As a consequence, magnetoelectric coupling effects in this type of split-order parameter multiferroic that were previously assigned to a pronounced 3d-4f coupling have now to be scrutinized with respect to their origin

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

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

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

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

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

Possible evidence for electromagnons in multiferroic manganites

Magnetodielectric materials are characterized by a strong coupling of magnetic and dielectric properties and in rare cases simultaneously exhibit both, magnetic and polar order. Among other multiferroics, TbMnO3 and GdMnO3 reveal a strong magneto-dielectric (ME) coupling and as a consequence fundamentally new spin excitations exist: Electro-active magnons, or electromagnons, i. e. spin waves which can be excited by ac electric fields. Here we show that these excitations appear in the phase with an incommensurate (IC) magnetic structure of the manganese spins. In external magnetic fields this IC structure can be suppressed and the electromagnons are wiped out, thereby inducing considerable changes in the index of refraction from dc up to THz frequencies. Hence, besides adding a new creature to the zoo of fundamental excitations, the refraction index can be tuned by moderate magnetic fields, which allows the design of a new generation of optical switches and optoelectronic devices.Comment: 4 Pages, 2 figure