"Peeling property" for linearized gravity in null coordinates

A complete description of the linearized gravitational field on a flat background is given in terms of gauge-independent quasilocal quantities. This is an extension of the results from gr-qc/9801068. Asymptotic spherical quasilocal parameterization of the Weyl field and its relation with Einstein equations is presented. The field equations are equivalent to the wave equation. A generalization for Schwarzschild background is developed and the axial part of gravitational field is fully analyzed. In the case of axial degree of freedom for linearized gravitational field the corresponding generalization of the d'Alembert operator is a Regge-Wheeler equation. Finally, the asymptotics at null infinity is investigated and strong peeling property for axial waves is proved.Comment: 27 page

CYK Tensors, Maxwell Field and Conserved Quantities for Spin-2 Field

Starting from an important application of Conformal Yano--Killing tensors for the existence of global charges in gravity, some new observations at \scri^+ are given. They allow to define asymptotic charges (at future null infinity) in terms of the Weyl tensor together with their fluxes through \scri^+. It occurs that some of them play a role of obstructions for the existence of angular momentum. Moreover, new relations between solutions of the Maxwell equations and the spin-2 field are given. They are used in the construction of new conserved quantities which are quadratic in terms of the Weyl tensor. The obtained formulae are similar to the functionals obtained from the Bel--Robinson tensor.Comment: 20 pages, LaTe

Rigid spheres in Riemannian spaces

Choice of an appropriate (3+1)-foliation of spacetime or a (2+1)-foliation of the Cauchy space, leads often to a substantial simplification of various mathematical problems in General Relativity Theory. We propose a new method to construct such foliations. For this purpose we define a special family of topological two-spheres, which we call "rigid spheres". We prove that there is a four-parameter family of rigid spheres in a generic Riemannian three-manifold (in case of the flat Euclidean three-space these four parameters are: 3 coordinates of the center and the radius of the sphere). The rigid spheres can be used as building blocks for various ("spherical", "bispherical" etc.) foliations of the Cauchy space. This way a supertranslation ambiguity may be avoided. Generalization to the full 4D case is discussed. Our results generalize both the Huang foliations (cf. \cite{LHH}) and the foliations used by us (cf. \cite{JKL}) in the analysis of the two-body problem.Comment: 23 page

Energy and angular momentum of the weak gravitational waves on the Schwarzschild background -- quasilocal gauge-invariant formulation

It is shown that the axial and polar perturbations of the spherically symmetric black hole can be described in a gauge-invariant way. The reduced phase space describing gravitational waves outside of the horizon is described by the gauge-invariant quantities. Both degrees of freedom fulfill generalized scalar wave equation. For the axial degree of freedom the radial part of the equation corresponds to the Regge-Wheeler result (Phys. Rev. 108, 1063-1069 (1957)) and for the polar one we get Zerilli result (Phys. Rev. D2, 2141-2160 (1970)), see also Chandrasekhar (The Mathematical Theory of Black Holes,(Clarendon Press Oxford, 1983)), Moncrief (Annals of Physics 88, 323-342 (1974)) for both. An important ingredient of the analysis is the concept of quasilocality which does duty for the separation of the angular variables in the usual approach. Moreover, there is no need to represent perturbations by normal modes (with time dependence $\exp(-ikt)$), we have fields in spacetime and the Cauchy problem for them is well defined outside of the horizon. The reduced symplectic structure explains the origin of the axial and polar invariants. It allows to introduce an energy and angular momentum for the gravitational waves which is invariant with respect to the gauge transformations. Both generators represent quadratic approximation of the ADM nonlinear formulae in terms of the perturbations of the Schwarzschild metric. We also discuss the boundary-initial value problem for the linearized Einstein equations on a Schwarzschild background outside of the horizon.Comment: 23 page

Orthorhombic phase of La0.5_{0.5}Bi0.5_{0.5}NiO3_{3} studied by first principles

The aim of presented first principles study of La$_{0.5}$Bi$_{0.5}$NiO$_{3}$ is to investigate electronic structure of orthorhombic phase Pbnm. The calculations show that metallicity and magnetism of the system are strongly related with hybridization between Ni 3d and O 2p. To improve the quality of the electronic structure description of the system, especially the treatment of correlation for the Ni 3d, we employ GGA, LDA, and GGA+U, LDA+U. The LSDA results give good agreement with experiment. Thus, the screening effects originating from the hybridized 3d and O 2p electrons are sufficiently strong that they reduce the electronic correlations in the La$_{0.5}$Bi$_{0.5}$NiO$_{3}$, making it a weakly correlated metal.Comment: 4 pages, 3 figures; The European Conference Physics of Magnetism 2017, submitted to Acta Physica Polonica

Parameters of a gas-solids JET in pneumatic powder injection into liquid alloys with a non-submerged lance

The paper presents powder injection into liquid alloys with a non-submerged lance. The parameters of the diphase gas-solids jet were found as the most important factor to achieve good efficiency of the process. If the parameters are improper, the jet will not penetrate the liquid and the solid particles will not be uniformly distributed. The jet cone profile is often crucial for diphase jet penetration, so this parameter was analyzed along with particle velocity on the lance outlet and the experiments proven this assumption. The use of a high-speed camera allowed to capture and analyze jet motion, which verified the data of previous authors and that in the literature. Experiments of both the model and real injection into molten cast iron proved both the mathematical model and numerical simulation