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

Solving the characteristic initial value problem for colliding plane gravitational and electromagnetic waves

A method is presented for solving the characteristic initial value problem for the collision and subsequent nonlinear interaction of plane gravitational or gravitational and electromagnetic waves in a Minkowski background. This method generalizes the monodromy transform approach to fields with nonanalytic behaviour on the characteristics inherent to waves with distinct wave fronts. The crux of the method is in a reformulation of the main nonlinear symmetry reduced field equations as linear integral equations whose solutions are determined by generalized (``dynamical'') monodromy data which evolve from data specified on the initial characteristics (the wavefronts).Comment: 4 pages, RevTe

Collision of plane gravitational and electromagnetic waves in a Minkowski background: solution of the characteristic initial value problem

We consider the collisions of plane gravitational and electromagnetic waves with distinct wavefronts and of arbitrary polarizations in a Minkowski background. We first present a new, completely geometric formulation of the characteristic initial value problem for solutions in the wave interaction region for which initial data are those associated with the approaching waves. We present also a general approach to the solution of this problem which enables us in principle to construct solutions in terms of the specified initial data. This is achieved by re-formulating the nonlinear dynamical equations for waves in terms of an associated linear problem on the spectral plane. A system of linear integral ``evolution'' equations which solve this spectral problem for specified initial data is constructed. It is then demonstrated explicitly how various colliding plane wave space-times can be constructed from given characteristic initial data.Comment: 33 pages, 3 figures, LaTeX. Accepted for publication in Classical and Quantum Gravit

Monodromy-data parameterization of spaces of local solutions of integrable reductions of Einstein's field equations

For the fields depending on two of the four space-time coordinates only, the spaces of local solutions of various integrable reductions of Einstein's field equations are shown to be the subspaces of the spaces of local solutions of the ``null-curvature'' equations constricted by a requirement of a universal (i.e. solution independent) structures of the canonical Jordan forms of the unknown matrix variables. These spaces of solutions of the ``null-curvature'' equations can be parametrized by a finite sets of free functional parameters -- arbitrary holomorphic (in some local domains) functions of the spectral parameter which can be interpreted as the monodromy data on the spectral plane of the fundamental solutions of associated linear systems. Direct and inverse problems of such mapping (``monodromy transform''), i.e. the problem of finding of the monodromy data for any local solution of the ``null-curvature'' equations with given canonical forms, as well as the existence and uniqueness of such solution for arbitrarily chosen monodromy data are shown to be solvable unambiguously. The linear singular integral equations solving the inverse problems and the explicit forms of the monodromy data corresponding to the spaces of solutions of the symmetry reduced Einstein's field equations are derived.Comment: LaTeX, 33 pages, 1 figure. Typos, language and reference correction

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

Einstein's equations and the chiral model

The vacuum Einstein equations for spacetimes with two commuting spacelike Killing field symmetries are studied using the Ashtekar variables. The case of compact spacelike hypersurfaces which are three-tori is considered, and the determinant of the Killing two-torus metric is chosen as the time gauge. The Hamiltonian evolution equations in this gauge may be rewritten as those of a modified SL(2) principal chiral model with a time dependent `coupling constant', or equivalently, with time dependent SL(2) structure constants. The evolution equations have a generalized zero-curvature formulation. Using this form, the explicit time dependence of an infinite number of spatial-diffeomorphism invariant phase space functionals is extracted, and it is shown that these are observables in the sense that they Poisson commute with the reduced Hamiltonian. An infinite set of observables that have SL(2) indices are also found. This determination of the explicit time dependence of an infinite set of spatial-diffeomorphism invariant observables amounts to the solutions of the Hamiltonian Einstein equations for these observables.Comment: 22 pages, RevTeX, to appear in Phys. Rev.

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

Oral Immunization of Wildlife Against Rabies: Concept and First Field Experiments

The possibility of immunizing carnivores against rabies with live attenuated vaccine administered by the oral route was raised by North American scientists in the 1960s. Subsequently, several American and European teams tested different vaccine strains in the laboratory for efficacy and safety and studied vaccine stabilization, vaccine delivery systems, baIt acceptance by wl1d ammals, and bait distribution schemes. The first field trial of a cloned SAD (Street Alabama Dufferin) strain in baits designed to immunize foxes orally ~as conducted in an Alpine valley in Switzerland in 1978. A population containing ∼60% immune foxes at the valley entrance stopped the spread of the disease into untreated upper parts of the valley. T~e strategic use of oral vaccination of foxes in additional regions of SWItzerland resulted m freedom from the zoonosis in four-fifths of the countr

Stress effect on magnetoimpedance (MI) in amorphous wires at GHz frequencies and application to stress-tunable microwave composite materials

The effect of tensile stress on magnetoimpedance (MI) in CoMnSiB amorphous wires at microwave frequencies (0.5-3 GHz) is investigated both experimentally and theoretically. In the presence of the dc bias magnetic field of the order of the anisotropy field, the impedance shows very large and sensitive change when the wire is subjected to a tensile stress: 100% and 60% per 180 MPa for frequencies 500 MHz and 2.5 GHz, respectively. It is demonstrated that this behavior owes mainly to the directional change in the equilibrium magnetization caused by the applied stress and field, which agrees well with the theoretical results for the surface impedance. This stress effect on MI is proposed to use for creating microwave stress-tunable composite materials containing short magnetic wires. The analysis of the dielectric response from such materials shows that depending on the stress level in the material, the dispersion of the effective permittivity can be of a resonant or relaxation type with a considerable change in its values (up to 100% at 600 MPa). This media can be used for structural stress monitoring by microwave contrast imaging