Singularities at real points of ℋ space

In the presence of gravitational radiation, there are ordinarily no shear-free slices of null infinity. A four-complex-dimensional set of shear-free slices of complexified null infinity do exist. They comprise the manifold space. In general, there are no preferred real subspaces of space associated with slices of real null infinity. However, for radiation fields possessing a twist-free axial symmetry, a two-parameter family of shear-free slices of real null infinity exist and therefore pick out a preferred two-dimensional real subspace of space. In this paper, we study the geometry of these 2-spaces for the particular case of quadrupole radiation fields for which determination of the shear-free slices reduces to the standard problem of determining orbits of a particle moving in a potential. Our principal interest is the investigation of possible singularities caused by sufficiently intense radiation fields. We find that such singularities do occur for radiation fields having the characteristic powerc ⁵/G.     

Solar system constraints on asymptotically flat IR modified Hořava gravity through light deflection

In this paper, we study the motion of photons around a Kehagias–Sfetsos (KS) black hole and obtain constraints on IR modified Ho?ava gravity without cosmological constant (~Λ _W ). An analytic formula for the light deflection angle is obtained. For a propagating photon, the deflection angle δφ increases with large values of the Ho?ava gravity parameter ω. Under the UV limit \({\omega \longrightarrow \infty}\), deflection angle reduces to the result of usual Schwarzschild case, 4GM/R. It is also found that with increasing scale of astronomical observation system the Ho?ava–Lifshitz gravity should satisfy |ω M ²| > 1.1725 × 10^?16 with 12% precision for Earth system, |ω M ²| > 8.27649 × 10^?17 with 17% precision for Jupiter system and |ω M ²| > 8.27650 × 10^?15 with 0.17% precision for solar system.     

Approximate ℋ spaces

We show how, for a wide class of asymptotically flat space-times, it is possible to solve the equation for asymptotically shear-free complex null cones (the good-cut equation) to first approximation, and thereby obtain first-order spaces and associated firstorder asymptotic projective twistor spaces.Dedicated to Achille Papapetrou on the occasion of his retirement.     

Vacuum polarization of scalar electrodynamics in flat space－time with nontrivial topology

The one-loop vacuum polarization is calculated for scalar electrodynamics in a flat space－time with the topology S¹×R³. The effect of vacuum polarization upon photon propagation is considered. It is found that photon propagation becomes anisotropic with some photon modes acquiring a positive topological mass and thus travelling at a subluminal speed.     

A new ℋ -space formalism

The equations governing geometrical objects in ? space are written in terms of operators adapted to families of left shear-freeσ ⁰= 0) cross sections of complexified null infinity (C I ⁺). The concept of ?-conformai weight (HCW) is introduced, and a derivative operatorI _a ^′ , which is closely connected with the covariant derivative but which (unlike the covariant derivative) maps objects having well-defined HCW to other such objects, is defined. A function ?, derived from the Gaussian curvature of left shear-free slicings ofC I ⁺ and having a well-defined HCW, is shown to contain all the curvature information for ? space.     

Nondiverging algebraically special ℋ-spaces

All nondiverging algebraically special -spaces are found by means of the complexified spin-coefficient formalism. The solutions are found to group naturally into two classes according to whether or not the optical-rotation spin coefficient vanishes.Research supported in part by a grant from the National Science Foundation.     

An efficient finite volume method for electric field–space charge coupled problems

The goal of this paper is to introduce some recently developed finite volume schemes to enable numerical simulation of electric field–space charge coupled problems. The key features of this methodology are the possibility of handling problems with complex geometries and accurately capturing the charge density distribution. The total variation diminishing (TVD) scheme and the improved deferred correction (IDC) scheme are used to compute the convective and diffusive fluxes respectively. Our technique is firstly verified with the computation of hydrostatic solutions in a two coaxial cylinders configuration. The homogeneous and autonomous injection from the inner or outer electrode is considered. Comparison has been made with the analytical solution. The numerical technique is also applied to the problem of corona discharge in a blade-plane configuration. The good agreement between our numerical solution and the one obtained with a combination approach of Finite Element Method (FEM) and Method of Characteristics (MoC) is shown.     

Is the standard model saved asymptotically by conformal symmetry?

Journal of Experimental and Theoretical Physics - It is pointed out that the top-quark and Higgs masses and the Higgs VEV with great accuracy satisfy the relations 4m 2 = 2m 2 = v 2, which are very...     

BΛF theory and flat spacetimes

We propose a reduced constrained Hamiltonian formalism for the exactly solubleBF theory of flat connections and closed two-forms over manifolds with topology ³ × (0,1). The reduced phase space variables are the holonomies of a flat connection for loops which form a basis of the first homotopy group ₁( ³), and elements of the second cohomology group of ³ with value in the Lie algebraL(G). WhenG=SO(3,1), and if the two-form can be expressed asB=ee, for some vierbein fielde, then the variables represent a flat spacetime. This is not always possible: We show that the solutions of the theory generally represent spacetimes with global torsion. We describe the dynamical evolution of spacetimes with and without global torsion, and classify the flat spacetimes which admit a locally homogeneous foliations, following thurston's classification of geometric structures.This research is supported in part by the National Science Foundation, Grant No. PHY 89-04035, by CONACyT Grant No. 400349-1714E (Mexico), and by the Association Générale pour la Coopération et le Développement (Belgium).     

Efficient high-power UV laser generated by an optimized flat–flat actively Q-switched laser with extra-cavity harmonic generations

We investigate the parasitic lasing effect in the high-power actively Q-switched laser with a flat–flat resonator. The parasitic lasing effect in the low-Q stage is found to lead to long tails in the output pulses, corresponding to the peak-power reduction. We experimentally determine the shortest cavity length without the parasitic lasing effect to optimize the performance of the high-power actively Q-switched laser with a flat–flat cavity. We further use the optimized fundamental laser to generate green and UV lasers by extra-cavity harmonic generations. At a pump power of 44 W, the output powers at 355 nm and 532 nm as high as 6.65 W and 8.38 W are obtained at a pulse repetition rate of 40 kHz.     

Landau analog levels for dipoles in non-commutative space and phase space

We investigate the analog of Landau quantization, for a neutral polarized particle in the presence of homogeneous electric and magnetic external fields, in the context of non-commutative quantum mechanics. This particle, possessing electric and magnetic dipole moments, interacts with the fields via the Aharonov–Casher and He–McKellar–Wilkens effects. For this model we obtain the Landau energy spectrum and the radial eigenfunctions of the non-commutative space coordinates and non-commutative phase space coordinates. Also we show that the case of non-commutative phase space can be treated as a special case of the usual non-commutative space coordinates.     

Frequency selective surface with a flat topped passband

Two frequency selective surface (FSS) configurations with flat topped passband are presented in this paper. One configuration is single layer FSS with,λ/4 thickness dielectric loaded on both sides,and the other is double layers FSS.Based on the modal matching method,the frequency response properties including angle effect and polarization effect of both FSS configurations are analyzed,and the plots of the frequency versus transmission coefficient are obtained for different incident angles and polarizations.It is shown that the structure with the single layer FSS embedded centrally in the ,k/2 thickness dielectric has a wider flat top bandwidth of 6.8 GHz than that of the double layers FSS of 3 GHz.In addition,the fabrication of single layer is relatively easier than the double layers FSS.     

Finiteness of Ricci flat supersymmetric non-linear σ-models

Combining the constraints of Kähler differential geometry with the universality of the normal coordinate expansion in the background field method, we study the ultraviolet behavior of 2-dimensional supersymmetric non-linear -models with target space an arbitrary riemannian manifoldM. We show that the constraint ofN=2 supersymmetry requires that all counterterms to the metric beyond one-loop order be cohomologically trivial. It follows that such supersymmetric non-linear -models defined on locally symmetric spaces are super-renormalizable and thatN=4 models are on-shell ultraviolet finite to all orders of perturbation theory.     

Thermodynamic properties of asymptotically Reissner–Nordström black holes

Motivated by possible relation between Born–Infeld type nonlinear electrodynamics and an effective low-energy action of open string theory, asymptotically Reissner–Nordström black holes whose electric field is described by a nonlinear electrodynamics (NLED) are studied. We take into account a four dimensional topological static black hole ansatz and solve the field equations, exactly, in terms of the NLED as a matter field. The main goal of this paper is investigation of thermodynamic properties of the obtained black holes. Moreover, we calculate the heat capacity and find that the nonlinearity affects the minimum size of stable black holes. We also use Legendre-invariant metric proposed by Quevedo to obtain scalar curvature divergences. We find that the singularities of the Ricci scalar in Geometrothermodynamics (GTD) method take place at the Davies points.     

Computer-generated moiré profilometry based on flat image demodulation

Optical Review - A computer-generated moiré profilometry based on flat image demodulation is proposed. A sinusoidal fringe pattern and its background light are modulated by two-frequency...     

Nonequilibrium fluctuations in μ space

The properties of fluctuations in space in or outside thermal equilibrium are obtained by solving hierarchies of equations derived either from the Liouville or the Master equation. In particular we study the one-, two-, etc., time correlation functions that describe the spatial and temporal behavior of the fluctuations in space. Explicit solutions are obtained for a dilute gas. The Langevin approach is briefly discussed. Our results are compared with those obtained in the extensive literature, which is reviewed in some detail.     

Conformally flat sources for the Linet–Tian spacetime

We investigate the matching, across cylindrical surfaces, of static cylindrically symmetric conformally flat spacetimes with a cosmological constant $\Lambda $ , satisfying regularity conditions at the axis, to an exterior Linet–Tian spacetime. We prove that for $\Lambda \le 0$ such matching is impossible. On the other hand, we show through simple examples that the matching is possible for $\Lambda >0$ . We suggest a physical argument that might explain these results.