Proof of a generalized Geroch conjecture for the hyperbolic Ernst equation

We enunciate and prove here a generalization of Geroch's famous conjecture concerning analytic solutions of the elliptic Ernst equation. Our generalization is stated for solutions of the hyperbolic Ernst equation that are not necessarily analytic, although it can be formulated also for solutions of the elliptic Ernst equation that are nowhere axis-accessible.Comment: 75 pages (plus optional table of contents). Sign errors in elliptic case equations (1A.13), (1A.15) and (1A.25) are corrected. Not relevant to proof contained in pape

Differentially rotating disks of dust: Arbitrary rotation law

In this paper, solutions to the Ernst equation are investigated that depend on two real analytic functions defined on the interval [0,1]. These solutions are introduced by a suitable limiting process of Backlund transformations applied to seed solutions of the Weyl class. It turns out that this class of solutions contains the general relativistic gravitational field of an arbitrary differentially rotating disk of dust, for which a continuous transition to some Newtonian disk exists. It will be shown how for given boundary conditions (i. e. proper surface mass density or angular velocity of the disk) the gravitational field can be approximated in terms of the above solutions. Furthermore, particular examples will be discussed, including disks with a realistic profile for the angular velocity and more exotic disks possessing two spatially separated ergoregions.Comment: 23 pages, 3 figures, submitted to 'General Relativity and Gravitation

Determination of the Far-Infrared Cosmic Background Using COBE/DIRBE and WHAM Data

Determination of the cosmic infrared background (CIB) at far infrared wavelengths using COBE/DIRBE data is limited by the accuracy to which foreground interplanetary and Galactic dust emission can be modeled and subtracted. Previous determinations of the far infrared CIB (e.g., Hauser et al. 1998) were based on the detection of residual isotropic emission in skymaps from which the emission from interplanetary dust and the neutral interstellar medium were removed. In this paper we use the Wisconsin H-alpha Mapper (WHAM) Northern Sky Survey as a tracer of the ionized medium to examine the effect of this foreground component on determination of the CIB. We decompose the DIRBE far infrared data for five high Galactic latitude regions into H I and H-alpha correlated components and a residual component. We find the H-alpha correlated component to be consistent with zero for each region, and we find that addition of an H-alpha correlated component in modeling the foreground emission has negligible effect on derived CIB results. Our CIB detections and 2 sigma upper limits are essentially the same as those derived by Hauser et al. and are given by nu I_nu (nW m-2 sr-1) < 75, < 32, 25 +- 8, and 13 +- 3 at 60, 100, 140, and 240 microns, respectively. Our residuals have not been subjected to a detailed anisotropy test, so our CIB results do not supersede those of Hauser et al. We derive upper limits on the 100 micron emissivity of the ionized medium that are typically about 40% of the 100 micron emissivity of the neutral atomic medium. This low value may be caused in part by a lower dust-to-gas mass ratio in the ionized medium than in the neutral medium, and in part by a shortcoming of using H-alpha intensity as a tracer of far infrared emission.Comment: 38 pages, 8 figures. Accepted for publication in Ap

Evidence of breakdown of the spin symmetry in diluted 2D electron gases

Recent claims of an experimental demonstration of spontaneous spin polarisation in dilute electron gases \cite{young99} revived long standing theoretical discussions \cite{ceper99,bloch}. In two dimensions, the stabilisation of a ferromagnetic fluid might be hindered by the occurrence of the metal-insulator transition at low densities \cite{abra79}. To circumvent localisation in the two-dimensional electron gas (2DEG) we investigated the low populated second electron subband, where the disorder potential is mainly screened by the high density of the first subband. This letter reports on the breakdown of the spin symmetry in a 2DEG, revealed by the abrupt enhancement of the exchange and correlation terms of the Coulomb interaction, as determined from the energies of the collective charge and spin excitations. Inelastic light scattering experiments and calculations within the time-dependent local spin-density approximation give strong evidence for the existence of a ferromagnetic ground state in the diluted regime.Comment: 4 pages, 4 figures, Revte

Dirichlet Boundary Value Problems of the Ernst Equation

We demonstrate how the solution to an exterior Dirichlet boundary value problem of the axisymmetric, stationary Einstein equations can be found in terms of generalized solutions of the Backlund type. The proof that this generalization procedure is valid is given, which also proves conjectures about earlier representations of the gravitational field corresponding to rotating disks of dust in terms of Backlund type solutions.Comment: 22 pages, to appear in Phys. Rev. D, Correction of a misprint in equation (4

Unconventional resistivity at the border of metallic antiferromagnetism in NiS2

We report low-temperature and high-pressure measurements of the electrical resistivity \rho(T) of the antiferromagnetic compound NiS_2 in its high-pressure metallic state. The form of \rho(T) suggests that metallic antiferromagnetism in NiS_2 is quenched at a critical pressure p_c=76+-5 kbar. Near p_c the temperature variation of \rho(T) is similar to that observed in NiS_{2-x}Se_x near the critical composition x=1 where the Neel temperature vanishes at ambient pressure. In both cases \rho(T) varies approximately as T^{1.5} over a wide range below 100 K. However, on closer analysis the resistivity exponent in NiS_2 exhibits an undulating variation with temperature not seen in NiSSe (x=1). This difference in behaviour may be due to the effects of spin-fluctuation scattering of charge carriers on cold and hot spots of the Fermi surface in the presence of quenched disorder, which is higher in NiSSe than in stoichiometric NiS_2.Comment: 7 page

Observables for spacetimes with two Killing field symmetries

The Einstein equations for spacetimes with two commuting spacelike Killing field symmetries are studied from a Hamiltonian point of view. The complexified Ashtekar canonical variables are used, and the symmetry reduction is performed directly in the Hamiltonian theory. The reduced system corresponds to the field equations of the SL(2,R) chiral model with additional constraints. On the classical phase space, a method of obtaining an infinite number of constants of the motion, or observables, is given. The procedure involves writing the Hamiltonian evolution equations as a single `zero curvature' equation, and then employing techniques used in the study of two dimensional integrable models. Two infinite sets of observables are obtained explicitly as functionals of the phase space variables. One set carries sl(2,R) Lie algebra indices and forms an infinite dimensional Poisson algebra, while the other is formed from traces of SL(2,R) holonomies that commute with one another. The restriction of the (complex) observables to the Euclidean and Lorentzian sectors is discussed. It is also shown that the sl(2,R) observables can be associated with a solution generating technique which is linked to that given by Geroch.Comment: 23 pages (LateX-RevTeX), Alberta-Thy-55-9