Algebraically special left-flat spaces and their associated space-times

In a recent paper it was shown how to construct, under certain circumstances, asymptotic (Newman-Unti) series expansions for the spin-coefficient variables for real space-times from data obtained from a given left-flat space in an appropriate frame. If these expansions represent asymptotically flat space-times the latter have the given left-flat space as their H space. The method was described in a frame in which the asymptotic left-shear was zero whereas was not. For the discussion of algebraically special left-flat spaces it is more convenient to have vanish and remain nonzero. In this paper we determine all algebraically special left-flat spaces with diverging rays, utilizing Penrose's conformal technique, and then show in detail how to find the “initial data” for the construction of asymptotic series expansions for the corresponding real space-times.     

Uncertainty principle and the horizon size of our universe

Quantum uncertainties prevent simultaneous measurement of the expansion factor S(t) and its time derivative . Consequently the Hubble size has an inherent uncertainty in the quantum state that describes the semiclassical evolution of the universe. We show that the quantum uncertainty in the Hubble size of the universe is amplified to unacceptably large values in any inflationary process.This essay received an honorable mention from the Gravity Research Foundation, 1986-Ed.     

Review: Hamiltonian Linearization of the Rest-Frame Instant Form of Tetrad Gravity in a Completely Fixed 3-Orthogonal Gauge: A Radiation Gauge for Background-Independent Gravitational Waves in a Post-Minkowskian Einstein Spacetime

In the framework of the rest-frame instant form of tetrad gravity, where the Hamiltonian is the weak ADM energy , we define a special completely fixed 3-orthogonal Hamiltonian gauge, corresponding to a choice of non-harmonic 4-coordinates, in which the independent degrees of freedom of the gravitational field are described by two pairs of canonically conjugate Dirac observables (DO) . We define a Hamiltonian linearization of the theory, i.e. gravitational waves, without introducing any background 4-metric, by retaining only the linear terms in the DO's in the super-hamiltonian constraint (the Lichnerowicz equation for the conformal factor of the 3-metric) and the quadratic terms in the DO's in . We solve all the constraints of the linearized theory: this amounts to work in a well defined post-Minkowskian Christodoulou-Klainermann space-time. The Hamilton equations imply the wave equation for the DO's , which replace the two polarizations of the TT harmonic gauge, and that linearized Einstein's equations are satisfied. Finally we study the geodesic equation, both for time-like and null geodesics, and the geodesic deviation equation.     

The equation of motion and gravitational radiation of a small extended spherically symmetric mass

On the basis of an approximation method developed in a previous paper the motion of an extended small mass on a gravitational background is investigated. The mass is described by a spherically symmetric rest mass distribution with some form of rigidity; the smallness of the mass is defined by the assumption that the radius of the mass is small compared with the change of the background . The equation of motion is yielded by integrating Einstein's conservation law of energy and momentum over the world tube of the mass. In the lowest mixed order (mixed of the background and the retarded potentials of the mass in lowest order) this equation is identical with the geodesic line linearized in . In the case when the motion on a static background generated by a localized matter distribution is finite, the gravitational radiation of the mass in lowest order is given.     

The equation of motion and gravitational radiation of an ideal fluid sphere moving in a gravitational background

On the basis of an approximation method developed in a previous paper the motion of an ideal fluid sphere in a weak gravitational background is investigated. The sphere is assumed to be small in the sense that its radius is small compared with the change of the background . Furthermore the deformations of the sphere when accelerated by the background are assumed to be small compared with the extension of the sphere in the absence of acceleration. In the lowest mixed order (mixed of the background and the retarded potentials of the sphere in lowest order) the equation of motion is yielded by integrating Einstein's conservation law of energy and momentum over the world-tube of the sphere. One obtains an equation of motion for the center of the sphere that is identical with the geodesic line linearized in . In the case of a static background of a localized matter distribution it is shown that Einstein's energy-momentum complex formed with the retarded potentials from the accelerated motion of the sphere in lowest order (lowest mixed order) leads to an outgoing radiation of gravitational energy. All radiation terms can be expressed in terms of the background and the world-line of the center of the sphere.     

BRS cohomology of the supertranslations inD=4

Supersymmetry transformations are a kind of square root of spacetime translations. The corresponding Lie superalgebra always contains the supertranslation operator . We find that the cohomology of this operator depends on a spin-orbit coupling in anSU(2) group and has a quite complicated structure. This spin-orbit type coupling will turn out to be basic in the cohomology of supersymmetric field theories in general.     

A Complete Set of Riemann Invariants

There are at most 14 independent real algebraic invariants of the Riemann tensor in a four-dimensional Lorentzian space. In the general case, these invariants can be written in terms of four different types of quantities: R , the real curvature scalar, two complex invariants I and J formed from the Weyl spinor, three real invariants I₆, I₇ and I₈ formed from the trace-free Ricci spinor and three complex mixed invariants K, L and M. Carminati and McLenaghan [5] give some geometrical interpretations of the role played by the mixed invariants in Einstein-Maxwell and perfect fluid cases. They show that 16 invariants are needed to cover certain degenerate cases such as Einstein-Maxwell and perfect fluid and show that previously known sets fail to be complete in the perfect fluid case. In the general case, the invariants I and J essentially determine the components of the Weyl spinor in a canonical tetrad frame; likewise the invariants I₆, I₇ and I₈ essentially determine the components of the trace-free Ricci spinor in a (in general different) canonical tetrad frame. These mixed invariants then give the orientation between the frames of these two spinors. The six real pieces of information in K, L and M are precisely the information needed to do this. A table is given of invariants which give a complete set for each Petrov type of the Weyl spinor and for each Segre type of the trace-free Ricci spinor This table involves 17 real invariants, including one real invariant and one complex invariant involving , and in some degenerate cases.     

Diffusion in a symmetric bistable potential: A variational approach

An approximation procedure for the solution of stochastic nonlinear equations, which was derived from a variational principle in a previous paper, is applied to the problem of a particle that diffuses in a symmetric bistable potential starting from the point of unstable equilibrium. The second moment and variance for the particle's position are calculated as functions of the timet. Good agreement is found with results recently obtained by Baibuzet al. from an approximate evaluation of a path integral expression for the probability density.     

Symmetry breaking in Landau gauge a comment to a paper by T. Kennedy and C. King

For the non-compact abelian lattice Higgs model in Landau gauge Kennedy and King (Princeton preprint, 1985) showed that the two point function does not decay in the Higgs phase. We generalize their methods to show that for the same range of parameters there are states parametrized by an angle [0, 2) such that and 0$$ " align="middle" border="0"> .     

Logarithmic Sobolev inequality for lattice gases with mixing conditions

Let denote the grand canonical Gibbs measure of a lattice gas in a cube of sizeL with the chemical potential and a fixed boundary condition. Let be the corresponding canonical measure defined by conditioning on . Consider the lattice gas dynamics for which each particle performs random walk with rates depending on near-by particles. The rates are chosen such that, for everyn andL fixed, is a reversible measure. Suppose that the Dobrushin-Shlosman mixing conditions holds for forall chemical potentials . We prove that for any probability densityf with respect to ; here the constant is independent ofn orL andD denotes the Dirichlet form of the dynamics. The dependence onL is optimal.Research partially supported by U.S. National Science Foundations grant 9403462, Sloan Foundation Fellowship and David and Lucile Packard Foundation Fellowship.     

Influence of a strong longitudinal static electric field on free carrier faraday effect in an n-type InSb at room temperature at submillimeter wave frequencies

The expression for free carrier Faraday rotation and for ellipticity , as the function of the applied parallel static electric field and static magnetic field for a given value of wave angular frequency and electron concentration N₀, are obtained and theoretically analyzed with the aid of one-dimensional linearized wave theory and Kane's non-parabolic isotropic dispersion law. It is shown that the maximum Faraday rotation occurs near the cyclotron resonance condition, which can be expressed as , where , , and . Here m^* and e denote the effective mass and charge of electron, respectively. _g is the forbidden bandgap of semiconductor. v₀ is the carrier drift velocity, which is a non-linear function of E₀ in high field condition. A possibility of a simple way of determining the non-linear v₀ vs E₀ characteristics of semiconductors by the measurement of Faraday rotation is also discussed.     

On General Plane Fronted Waves. Geodesics

A general class of Lorentzian metrics, , , with any Riemannian manifold, is introduced in order to generalize classical exact plane fronted waves. Here, we start a systematic study of their main geodesic properties: geodesic completeness, geodesic connectedness and multiplicity causal character of connecting geodesics. These results are independent of the possibility of a full integration of geodesic equations. Variational and geometrical techniques are applied systematically. In particular, we prove that the asymptotic behavior of H(x,u) with x at infinity determines many properties of geodesics. Essentially, a subquadratic growth of H ensures geodesic completeness and connectedness, while the critical situation appears when H(x,u) behaves in some direction as , as in the classical model of exact gravitational waves.     

On the Product of Real Spectral Triples

The product of two real spectral triples and , the first of which is necessarily even, was defined by A.Connes as given by and, in the even-even case, by . Generically it is assumed that the real structure obeys the relations , , , where the -sign table depends on the dimension n modulo 8 of the spectral triple. If both spectral triples obey Connes' >-sign table, it is seen that their product, defined in the straightforward way above, does not necessarily obey this -sign table. In this Letter, we propose an alternative definition of the product real structure such that the -sign table is also satisfied by the product.     

The causal boundary of space-times

A definition of a causal boundary is given by assigning a future and a past endpoint to any non-extensible timelike or null line. A topology and a partial ordering can be introduced on . The usual conditions for the causal structure can be formulated as properties of . This boundary is compared with other types of boundaries.Read on 15 May 1970 at the Gwatt Seminar on the Bearings of Topology upon General RelativityWork supported by the Deutsche Forschungsgemeinschaft.     

Thermoelectric power of YBa2Cu3Ox in equilibrium with gas phases

Thermoelectric power (TP) and electrical conductivity (EC) measurements were performed for YEa₂Cu₃O_x at 1128 K under controlled oxygen partial pressure varying between 50 and 10⁵ Pa. Three regimes are observed for the electrical properties. At low both TP and EC remain constant with . In the medium range sharp changes of both electrical parameters occur; TP changes sign from positive above 4×10² Pa to negative below this value. In the high region (>7.6×10³ Pa) TP vs log exhibits two slopes; 5.1 below 1.5×10⁴ Pa and 8.4 above this value. The slopes can be discussed in terms of the defect structure involving singly and doubly ionized oxygen vacancies below and above 7.6×10³ Pa, respectively.     

Symmetries and Modular Intersections of Von Neumann Algebras

Let be von Neumann algebras acting on a Hilbert space and let be a common cyclic and separating vector. We say that have the modular intersection property with respect to if(1) -half-sided modular inclusions,(2) (If (1) holds the strong limit exists.) We show that under these conditions the modular groups of and generate a 2-dim. Lie group.This observation is the basis for obtaining group representations of Sl(2, )/Z ₂ generated by modular groups.     

CP-violating effects inZ decays to τ leptons

We calculate CP-odd correlations inZ decays to leptons, . These correlations are sensitive to the weak dipole moment of the . With 10⁷ producedZ particles and with observation of the decay channels and v we estimate that can be determined with an accuracy of about (1 s.d.).     

Superplasticity in A Zn-1·1 wt. % Al alloy

In the paper the results of the deformation behaviour study in a fine-grained Zn-1·1 wt. % Al alloy are presented. The influence of strain rate ranging from 4·2×10^–5 to 4·2×10^–2 s^–1 on the true stress — true strain curves, ductility and strain rate sensitivity was investigated at temperatures 295 K and 375 K. At both temperatures the superplastic behaviour was observed. The increase in temperature improved the superplastic properties and shifted the region of the superplastic behaviour to higher strain rates. The maximum values of ductilityA=700% and strain rate sensitivity parameter m=0·48 were established at 375 K at strain rates . The true stress — true strain curves were found to be influenced by a grain growth taking place during the deformation. The grain growth was also found to be responsible for significant differences in the parameterm values obtained from the log plots and from the strain rat-changes.     

On the blow-up of solutions of the 3-D Euler equations in a bounded domain

It is shown that if [0, ) is the maximal interval of existence of a smooth solutionu of the incompressible Euler equations in a bounded, simply connected domain R ³, then , where =×u is the vorticity. Crucial to this result is a special estimate proven in of the maximum velocity gradient in terms of the maximum vorticity and a logarithmic term involving a higher norm of the vorticity.     

The Chern classes of Sobolev connections

AssumeF is the curvature (field) of a connection (potential) onR ⁴ with finiteL ² norm . We show the chern number (topological quantum number) is an integer. This generalizes previous results which showed that the integrality holds forF satisfying the Yang-Mills equations. We actually prove the natural general result in all even dimensions larger than 2.