Four-parametric regular black hole solution

We present a regular class of exact black hole solutions of the Einstein equations coupled with a nonlinear electrodynamics source. For weak fields the nonlinear electrodynamics becomes the Maxwell theory, and asymptotically the solutions behave as the Reissner–Nordström one. The class is endowed with four parameters, which can be thought of as the mass m, charge q, and a sort of dipole and quadrupole moments and , respectively. For 3, 4, and |q|2s _c m the corresponding solutions are regular charged black holes. For = 3, they also satisfy the weak energy condition. For = = 0 we recover the Reissner–Nordström singular solution and for = 3, = 4 the family includes a previous regular black hole reported by the authors.     

The conceptual analysis (CA) method in theories of microchannels: Application to quantum theory. Part I. Fundamental concepts

A method is proposed that should facilitate the construction of theories of submicroscopic particles (denoted as theories of microchannels) in a way similar to the use of group-theoretical methods. The conceptual analysis (CA) method is based on the analysis of the basic concepts of a theory; it permits a determination of necessary conditions imposed on the mathematical apparatus (of the theory) which then appear as a mathematical representation of the structures obtained in a formal scheme of a theory. A pertinent conceptual analysis leads to a new definition (relativization) of the concept empirical implication. The approach may be characterized as realistic and operational. The application of the CA method is illustrated on the example of quantum theory. In Part I the algebraic structure of a partially ordered, up-ward directed, bounded set is deduced from the rudimentary concepts. In Parts II and III, we shall deduce the Hilbert-space structure (well established in quantum mechanics) from postulates on some essential idealizations accepted in the theory. Whereas Part II is concerned with the idealizations of existing quantum theories based on the Hilbert-space formalism, Part I may be considered as a general basis for a wider class of theories.Dedicated to Prof. G. Ludwig on the occasion of his 60th birthday.     

Stationary states of an electron in the field of a hole in an ionic crystal

An approximate solution is given of the Schrödinger equation for S-states of an electron in the field of a hole, when the potential energy of the electron has the form — e²/r [1+exp (–qr].

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s- , –e²/r [1+exp (–qr].

     

Changes in EPR spectrum of free radical species inγ-irradiated polyformaldehyde

We have found that gamma-irradiated polyformaldehyde does not exhibit the effect of the disappearance of the hyperfine structure of EPR spectrum as a function of the dose or the time passed since the end of irradiation, as was found earlier for a group of polymers having only C-C-C-C-atoms in the polymer chain. This difference in the change in the EPR of the polyformaldehyde (PFA) spectrum compared with the polymers with a -C-C-C-C- chain is explained by the impossibility of forming a conjugate double bond in the -C-O-C-O- chain in PFA.

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, , -, , , atom C-C-C-C-. ( ) C-C-C-C- , C-O-C-O- qu .

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The author thanks K. Vacek for many valuable discussions which helped this work.     

An asymptotically flat ℋ space

The null geodesic equation is solved for the space of Sparling and Tod. Bondi coordinates are found and it is verified that the space construction is idempotent, i.e., the -space of this space is itself, symbolically ² = . Properties of the solution are used to motivate a definition of asymptotic flatness.S.R.C. Postdoctoral Research Fellow.     

Entropy,the central limit theorem and the algebra of the canonical commutation relation

The central limit theorem of Cushen and Hudson is reformulated on the algebra of the CCR. Namely, for a gauge invariant state , the weighted convolutions _n of the central limit tend to the quasi-free reduction _Q of pointwise. It is proved that if the initial relative entropy S(, _Q ) is finite, then S( _n , _Q ) goes to 0 and so _n – _Q 0. No restriction on the dimension of the test function space is made.     

ЭЛЕКТРИЧЕСКАЯ ЭКВИВ АЛЕНТНАЯ СХЕМА ЗАТУХАЮЩИХ КОЛЕБАНИ Й ИЗГИБА У ПБЕЗОЭЛЕКТРИЧЕСКИ Х СТЕРЖНЕЙ

- .     

Gravitation and universal Fermi coupling in general relativity

The generally covariant Lagrangian densityG = + 2K _matter of the Hamiltonian principle in general relativity, formulated by Einstein and Hilbert, can be interpreted as a functional of the potentialsg _ikand of the gravitational and matter fields. In this general relativistic interpretation, the Riemann-Christoffel form _kl ⁱ = _kl ⁱ for the coefficients _kl ⁱ of the affine connections is postulated a priori. Alternatively, we can interpret the LagrangianG as a functional of , g_ik, and the coefficients _kl ⁱ . Then the _kl ⁱ are determined by the Palatini equations. From these equations and from the symmetry _kl ⁱ = _lk ⁱ for all matter fields with /=0 the Christoffel symbols again result. However, for Dirac's bispinor fields, / becomes dependent on the Dirac current, essentially with a coupling factor Khc. In this case, the Palatini equations define a new transport rule for the spinor fields, according to which a second universal interaction results for the Dirac spinors, besides Einstein's gravitation. The generally covariant Dirac wave equations become the general relativistic nonlinear Heisenberg wave equations, and the second universal interaction is given by a Fermi-like interaction term of the V-A type. The geometrically induced Fermi constant is, however, very small and of the order 10^–81erg cm³     

The influence of the spectral asymmetry of X-ray emission lines on the results of studying defects in crystals by X-rays of different wavelength

Since the asymmetry of X-ray emission lines was found to influence the exact measurements of lattice parameters of powdered samples the author has revised the results she once obtained when carrying out exact measurements of the lattice parameter with radiations of various wavelengths for tungsten crystals containing admixtures of different elements. It is shown that with samples having an inhomogeneous distribution of the admixtures in the crystals the typical graphs of lattice parameter found originally remain when respecting the influence of the spectral asymmetry. On the other hand, with a sintered sample which has been homogeneized by long annealing the introduction of corrections to spectral asymmetry leads to an adjustment of the differences measured originally, for which it was difficult to find a probable explanation.

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, . , , . , , , , , , .

     

From where do quantum groups come?

The phase space realizations of quantum groups are discussed using *-products. We show that on phase space, quantum groups appear necessarily as two-parameter deformation structures, one parameter (v) being concerned with the quantization in phase space, the other () expressing the quantum groups as deformation of their Lie counterparts. Introducing a strong invariance condition, we show the uniqueness of the -deformation. This suggests that the strong invariance condition is a possible origin of the quantum groups.Dedicated to Asim Barut with all our friendship.     

A search for moment localisation in UMn2

SR, high resolution neutron powder diffraction and heat capacity have been used to study the spin fluctuation compound UMn₂. The SR spectra are dominated by muon depolarisation due to static fields from the Mn nuclei, features in the temperature dependence of the associated relaxation rate, , correlating well with the structural transitions observed at 210K. While a weak exponential relaxation ( 0.01s^–1) indicates the presence of atomic spin fluctuations between 50K and 325K, SR provides little evidence of moment localisation or long range magnetic order, although an anomalous increase in below 40K is observed.     

Quantum Mixtures in the Early Universe

In Relativistic Schrödinger Theory for spinning matter, there exist mixtures which have vanishing spin density (S 0). Such a fermionic, but spinless quantum fluid is studied in detail. Its energy-momentum density can develop negative pressure which is able to accelerate the expansion of the universe and to create matter energy through continuous bouncing at minimal radius (cosmic pumping).     

Acoustomagnetoelectric current effects on mesoultrasound in anisotropic semiconductors

The acoustomagnetoelectric (AME) current effects on mesoultrasound in monopolar single-valley semiconductors with anisotropic scattering in arbitrary classical magnetic fields are computed analytically. The specimen is considered short-circuited along the q-wave vector of the ultrasound (US) wave. Two configurations are examined: 1) q is directed at an arbitrary angle 9 to the axis of highest order crystal symmetry C₆ (z axis), the y axis to the (q, C₆) plane, the magnetic field B lies in the (q, y) plane at an arbitrary angle to the vector q. Two transverse AME field components are calculated: along y and in the (q, C₆) plane. They express the Hall effects at mesoultrasound, the planar and normal, 2) q is directed along the y axis while B is in the (x, z) plane at an angle to the C₆(z) axis. The AME field component along B, the Grobner effect at mesoultrasound, is calculated. The dependence of the effects onB is studied and their estimate is given in weak and strong fields.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 57–61, July, 1989.     

The problem of the imperfection of a world,itself created by a perfect god

The two main arguments concern(1) the presence of an enlightened complementarity between philosophic (including scientific) and religious (not including mystic) thought, and(2) the necessity to postulate a threefold relationship whenever one is to gain knowledge of any kind. They are both inspired by physics (from Bohr's strict complementarity, resp. from Newton's fundamental postulate).God's perfection resides at least in Symmetry in a generalized (not restrictively spatial) sense. Yet, as the argument goes, Space does not exist as a thing. Consequently, the Great Geometer (God) cannot dwell within a World He creates, and it is wrong to speak about His (God's) existence; for, existence is bound to the temporal, and Time is, together with the World, part of God's creation. Thus the only possible creation consists in God separating World and Time from Himself: This is the paradigm of Symmetry-breaking.Polytheistic mythologies all assume such and such imperfection of their deities; hence perfection is meaningful for monotheism only. A relationship of a threefold (trinitary) nature must then obtain between God, World, and Time; this is analogous to Newton's postulate relating force, momentum and time. Just as the latter and its specific generalizations must be found true by verification, the said threefold relationship must also be found true: within philosophic thoughtmore geometrico (in a generalized sense), within religious thoughtmore hymnometrico. Yet the complementarity (called enlightened) arising between the two kinds of thought is of a higher nature than Bohr's strict complementarity. While it can be understood from the role assumed by language itself, it can however only be disposed of within mystic contemplation.Dedicated to Sir KARL POPPER on the occasion of his 90th birthday.     

On the geometric structure underlying the eikonal equation

Given the eikonal equation _i=1 ³ (/x ⁱ ) ² =n ², we investigate the geometric structure that underlies the law of propagation of the wavefronts (x ¹,x ²,x ³) —ct=0. It turns out that Huygens' principle for the propagation of wavefronts is given in terms of a contact structure. Wavefronts are carried into wavefronts by contact transformations. As regards the wave-particle duality principle that arises in quantum mechanics, there is a natural geometric structure, a symplectic manifold (M ²ⁿ , ), which unifies Fermat's principle and the eikonal equation (Huygens' principle).On leave of absence from Institut für Angewandte Mathematik, Fachbereich Mathematik der Universität Mainz, Mainz, German Federal Republic.     

Low-temperature and long-time anomalies of a damped quantum particle

The time evolution of a damped quantum particle is discussed. Dissipation is modeled by the bilinear coupling to a set of harmonic oscillators. Using a functional integral technique that accounts for initial correlations between the particle and the reservoir, one can express the dynamics of the damped particle entirely in terms of equilibrium correlation functions. The long-time behavior of these correlations is determined for memory damping arising from the coupling to a reservoir with spectral densityI() at low frequencies, where > 0. The time evolution of nonequilibrium initial states of the damped particle is discussed. At finite temperatures an initially localized state is found to spread subdiffusively or superdiffusively, depending on . For > 2 the damping becomes ineffective for long times, and the width of a state grows kinematically. At zero temperature and for < 1, an initially localized state remains localized for all times. For 1 the state spreads, but with a slower rate than at finite temperatures. Study of arbitrary initial states indicates that the process is ergodic at finite temperatures only for 2 and at zero temperature for 1 2.     

An experiment to test an explanation of a possible violation of quantum theory

An experiment to test a possible explanation of the Schmidt backwards causation results is suggested. The experiment might distinguish between many- and one- world interpretations of quantum theory.     

On the Effect of Increasing the Radiative-Transition Rate Near a Nanosize Point

A short review of theoretical and experimental studies concerning the photoexcited florescence and Raman scattering of light for a substance in a space containing small material bodies is presented. Calculations of the radiativetransition probability for atoms (molecules) in the vicinity of bodies with a size much smaller than the light wavelength are performed. The probabilities of the singlephoton and doublephoton transitions are shown to increase by factors of 9 and 81 in the vicinity of a nanosize sphere with dielectric constant ||\ 1. The probability of a radiative transition in the vicinity of the vertex of a conic needle bearing up against a plane (both with || 1) increases by factors of (/R _in)² and (/R _in)⁴ for singlephoton and doublephoton transitions, respectively (R _in is the curvature radius for the needle vertex). This theoretical result is suggested as an explanation of the effect of increasing the radiation process intensity in the experiments carried out in the studies cited below.     

Some properties of topological geons

We investigate the Finkelstein-Misner geons for a non-simply-connected space-time manifold (M, g ₀). We use relations between different Lorentzian structures unequivalent tog ₀ and topological properties ofM given by the Morse theory. It implies that to some pieces of geons we have to associate Wheeler's worm-holes. Geons that correspond to time-orientable Lorentz structures are related tog ₀ by Morse functions that describe the attaching of a handle of index one. In the case of geons associated to time-nonorientable Lorentzian structures, appropriate handles are related to loops along which the notion of time reverses. If we assume electromagnetic properties of geons, then only four species, v, e, p, m, of different geons can exist and geon m has to decay according to mv+p+e.     

The temperature vibrations of urea molecules

The structural and dynamic parameters of urea at 112°K and 295°K were determined by the least squares method. The characteristic temperature of the torsional optical vibrations of a molecule about a C-O bond was determined and is in good agreement with the value determined by Raman scattering. The fractional X-coordinate of the nitrogen atom corrected for torsional vibrations was determined and it was found that the magnitude of the projection of the C-N bond in the given temperature range changes only within the limits of observational errors. A new method, called temperature difference synthesis, is described and it is shown that it is suitable for rapid qualitative determination of the thermal anisotropy of the vibrations of atoms in a crystal lattice.

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112°K 295°K. C-O , , . X- , C-N . , , , .