How can exact and approximate solutions of Einstein's field equations be compared?

The problem of comparison of the stationary axisymmetric vacuum solutions obtained within the framework of exact and approximate approaches for the description of the same general relativistic systems is considered. We suggest two ways of carrying out such comparison: (i) through the calculation of the Ernst complex potential associated with the approximate solution whose form on the symmetry axis is subsequently used for the identification of the exact solution possessing the same multipole structure, and (ii) the generation of approximate solutions from exact ones by expanding the latter in series of powers of a small parameter. The central result of our paper is the derivation of the correct approximate analogues of the double-Kerr solution possessing the physically meaningful equilibrium configurations. We also show that the interpretation of an approximate solution originally attributed to it on the basis of some general physical suppositions may not coincide with its true nature established with the aid of a more accurate technique.Comment: 32 pages, 5 figure

Remarks on the Charged, Magnetized Tomimatsu-Sato δ=2\delta=2 Solution

The full metric describing a charged, magnetized generalization of the Tomimatsu-Sato (TS) $\delta=2$ solution is presented in a concise explicit form. We use it to investigate some physical properties of the solution; in particular, we point out the existence of naked ring singularities in the hyperextreme TS metrics, the fact previously overlooked by the researchers, and we also demonstrate that the ring singularities can be eliminated by sufficiently strong magnetic fields in the subextreme case, while in the hyperextreme case the magnetic field can move singularities to the equatorial plane.Comment: 12 pages, 3 ps figures, LaTeX with epsf style (necessary files are included

Bell's inequalities in the tomographic representation

The tomographic approach to quantum mechanics is revisited as a direct tool to investigate violation of Bell-like inequalities. Since quantum tomograms are well defined probability distributions, the tomographic approach is emphasized to be the most natural one to compare the predictions of classical and quantum theory. Examples of inequalities for two qubits an two qutrits are considered in the tomographic probability representation of spin states.Comment: 11 pages, comments and references adde

Frame dragging, vorticity and electromagnetic fields in axially symmetric stationary spacetimes

We present a general study about the relation between the vorticity tensor and the Poynting vector of the electromagnetic field for axially symmetric stationary electrovacuum metrics. The obtained expressions allow to understand the role of the Poynting vector in the dragging of inertial frames. The particular case of the rotating massive charged magnetic dipole is analyzed in detail. In addition, the electric and magnetic parts of the Weyl tensor are calculated and the link between the later and the vorticity is established. Then we show that, in the vacuum case, the necessary and sufficient condition for the vanishing of the magnetic part is that the spacetime be static.Comment: 16 pages Latex. Some minor changes in the text and typos correcte

Evaluation of RGB-D Multi-Camera Pose Estimation for 3D Reconstruction

Advances in visual sensor devices and computing power are revolutionising the interaction of robots with their environment. Cameras that capture depth information along with a common colour image play a significant role. These devices are cheap, small, and fairly precise. The information provided, particularly point clouds, can be generated in a virtual computing environment, providing complete 3D information for applications. However, off-the-shelf cameras often have a limited field of view, both on the horizontal and vertical axis. In larger environments, it is therefore often necessary to combine information from several cameras or positions. To concatenate multiple point clouds and generate the complete environment information, the pose of each camera must be known in the outer scene, i.e., they must reference a common coordinate system. To achieve this, a coordinate system must be defined, and then every device must be positioned according to this coordinate system. For cameras, a calibration can be performed to find its pose in relation to this coordinate system. Several calibration methods have been proposed to solve this challenge, ranging from structured objects such as chessboards to features in the environment. In this study, we investigate how three different pose estimation methods for multi-camera perspectives perform when reconstructing a scene in 3D. We evaluate the usage of a charuco cube, a double-sided charuco board, and a robot’s tool centre point (TCP) position in a real usage case, where precision is a key point for the system. We define a methodology to identify the points in the 3D space and measure the root-mean-square error (RMSE) based on the Euclidean distance of the actual point to a generated ground-truth point. The reconstruction carried out using the robot’s TCP position produced the best result, followed by the charuco cuboid; the double-sided angled charuco board exhibited the worst performance

Impact of the «Simbiter» group multiprobiotics on the contents of monomers of bindweb structures in the periodontal tissues in conditions of prolonged hypoacidity

In conditions of prolonged omeprazole-induced hypoacidity in the periodontal tissues of rats an increased catabolism of collagenous and non- collagenous proteins is occurred, The "Simbiter acidophilic concentrated" and "Simbiter-omega" multiprobiotics prevent depolymerization of collagenous and non-collagenous structures of periodontal connective tissues of rats in conditions of prolonged hypoacidity

Coherent states for Hamiltonians generated by supersymmetry

Coherent states are derived for one-dimensional systems generated by supersymmetry from an initial Hamiltonian with a purely discrete spectrum for which the levels depend analytically on their subindex. It is shown that the algebra of the initial system is inherited by its SUSY partners in the subspace associated to the isospectral part or the spectrum. The technique is applied to the harmonic oscillator, infinite well and trigonometric Poeschl-Teller potentials.Comment: LaTeX file, 26 pages, 3 eps figure

General-relativistic Model of Magnetically Driven Jet

The general scheme for the construction of the general-relativistic model of the magnetically driven jet is suggested. The method is based on the usage of the 3+1 MHD formalism. It is shown that the critical points of the flow and the explicit radial behavior of the physical variables may be derived through the jet ``profile function."Comment: 12 pages, LaTex, no figure

Energy Release During Disk Accretion onto a Rapidly Rotating Neutron Star

The energy release L_s on the surface of a neutron star (NS) with a weak magnetic field and the energy release L_d in the surrounding accretion disk depend on two independent parameters that determine its state (for example, mass M and cyclic rotation frequency f) and is proportional to the accretion rate. We derive simple approximation formulas illustrating the dependence of the efficiency of energy release in an extended disk and in a boundary layer near the NS surface on the frequency and sense of rotation for various NS equations of state. Such formulas are obtained for the quadrupole moment of a NS, for a gap between its surface and a marginally stable orbit, for the rotation frequency in an equatorial Keplerian orbit and in the marginally stable circular orbit, and for the rate of NS spinup via disk accretion. In the case of NS and disk counterrotation, the energy release during accretion can reach $0.67\dot{M}c^2$. The sense of NS rotation is a factor that strongly affects the observed ratio of nuclear energy release during bursts to gravitational energy release between bursts in X-ray bursters. The possible existence of binary systems with NS and disk counterrotation in the Galaxy is discussed. Based on the static criterion for stability, we present a method of constructing the dependence of gravitational mass M on Kerr rotation parameter j and on total baryon mass (rest mass) m for a rigidly rotating neutron star. We show that all global NS characteristics can be expressed in terms of the function M(j, m) and its derivatives.Comment: 42 pages, 12 figures, to appear in Astronomy Letters, 2000, v.26, p.69

Strange meson production in Al+Al collisions at 1.9A GeV

The production of K$^+$, K$^-$ and $\varphi$(1020) mesons is studied in Al+Al collisions at a beam energy of 1.9A GeV which is close or below the production threshold in NN reactions. Inverse slopes, anisotropy parameters, and total emission yields of K$^{\pm}$ mesons are obtained. A comparison of the ratio of kinetic energy distributions of K$^-$ and K$^+$ mesons to the HSD transport model calculations suggests that the inclusion of the in-medium modifications of kaon properties is necessary to reproduce the ratio. The inverse slope and total yield of $\phi$ mesons are deduced. The contribution to K$^-$ production from $\phi$ meson decays is found to be [17 $\pm$ 3 (stat) $^{+2}_{-7}$ (syst)] %. The results are in line with previous K$^{\pm}$ and $\phi$ data obtained for different colliding systems at similar incident beam energies.Comment: 16 pages, 11 figure