Do we know the mass of a black hole? Mass of some cosmological black hole models

Using a cosmological black hole model proposed recently, we have calculated the quasi-local mass of a collapsing structure within a cosmological setting due to different definitions put forward in the last decades to see how similar or different they are. It has been shown that the mass within the horizon follows the familiar Brown–York behavior. It increases, however, outside the horizon again after a short decrease, in contrast to the Schwarzschild case. Further away, near the void, outside the collapsed region, and where the density reaches the background minimum, all the mass definitions roughly coincide. They differ, however, substantially far from it. Generically, we are faced with three different Brown–York mass maxima: near the horizon, around the void between the overdensity region and the background, and another at cosmological distances corresponding to the cosmological horizon. While the latter two maxima are always present, the horizon mass maxima is absent before the onset of the central singularity.     

One-dimensional model of inhomogeneous shear in sliding

The paper briefly describes a one-dimensional dynamic model of plastic shear deformation in a material surface layer in sliding friction, giving grounds to the reduction of the problem dimension from 3D to 1D. A selection of simulation results is presented to illustrate the peculiarities of plastic deformation under the action of two competitive processes — work hardening and thermal softening due to frictional heating. Presented also are experimental data on which to base the conclusion on the possibility of surface layer flow similar to flow of a viscous fluid. To assess from the Reynolds number whether turbulization of the surface layer is feasible, simulation results are used.     

SICs and Algebraic Number Theory

We give an overview of some remarkable connections between symmetric informationally complete measurements (SIC-POVMs, or SICs) and algebraic number theory, in particular, a connection with Hilbert’s 12th problem. The paper is meant to be intelligible to a physicist who has no prior knowledge of either Galois theory or algebraic number theory.     

Models of spherical shells as sources of Majumdar–Papapetrou type spacetimes

By starting with a seed Newtonian potential–density pair we construct relativistic thick spherical shell models for a Majumdar–Papapetrou type conformastatic spacetime. As a simple example, we considerer a family of Plummer–Hernquist type relativistic spherical shells. As a second application, these structures are then used to model a system composite by a dust disk and a halo of matter. We study the equatorial circular motion of test particles around such configurations. Also the stability of the orbits is analyzed for radial perturbation using an extension of the Rayleigh criterion. The models considered satisfying all the energy conditions.     

Gravitational and electromagnetic signatures of accretion into a charged black hole

We present the derivation and the solutions to the coupled electromagnetic and gravitational perturbations with sources in a charged black hole background. We work in the so called ghost gauge and consider as source of the perturbations the infall of radial currents. In this way, we study a system in which it is provoked a response involving both, gravitational and electromagnetic waves, which allows us to analyze the dependence between them. We solve numerically the wave equations that describe both signals, characterize the waveforms and study the relation between the input parameters of the infalling matter with those of the gravitational and electromagnetic responses.     

Synthesis,Optical Investigation and Biological Properties of Europium(III) Complexes with 2-(4-Chlorophenyl)-1-(2-Hydroxy-4-Methoxyphenyl)Ethan-1-one and Ancillary Ligands

Synthesis and photoluminescence behaviour of six novel europium complexes with novel β-hydroxyketone ligand, 2-(4-chlorophenyl)-1-(2-hydroxy-4-methoxyphenyl)ethan-1-one (CHME) and 2,2′-bipyridine (bipy) or neocuproine (neo) or 1,10-phenanthroline (phen) or 5,6-dimethyl-1,10-phenanthroline (dmphen) or bathophenanthroline (bathophen) were reported in solid state. The free ligand CHME and europium complexes, Eu(CHME)₃.2H₂O [1] Eu(CHME)₃.bipy [2], Eu(CHME)₃.neo [3], Eu(CHME)₃.phen [4], Eu(CHME)₃.dmphen [5] and Eu(CHME)₃.bathophen [6]were characterized by elemental analysis, FT-IR and ¹H-NMR. The photoluminescence emission spectra exhibited four characteristic peaks arising from the ⁵D₀ → ⁷F_J (J = 1–4) transitions of the europium ion in the solid state on monitoring excitation at λ_ex = 395 nm. The luminescence decay curves of these europium complexes possess single exponential behaviour indicating the presence of a single luminescent species and having only one site symmetry in the complexes. The luminescence quantum efficiency (η) and the experimental intensity parameters, Ω ₂ and Ω ₄ of europium complexes have also been calculated on the basis of emission spectra and luminescence decay curves. In addition, the antimicrobial and antioxidant activities were also studied of the investigated complexes.     

Substituent Effect on Absorption and Fluorescence Properties of Thieno[3, 2-<Emphasis Type="Italic">c</Emphasis>]Pyridine Derivatives

New substituted thieno[3,2-c]pyridine derivatives 5 were synthesized by the reaction of 3-bromo-4-chlorothieno[3,2-c]pyridine 1 with cyclic amine 2, which further on Suzuki reaction with boronic acids 4 converted to corresponding 3-arylthieno[3,2-c]pyridine 5. Substituent R³ has predominant effect on fluorescence properties of thienopyridines. However, the electron donor amine at C₄ has no effect on fluorescence properties of thienopyridines.

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Graphical Abstract New thieno[3,2-c]pyridine derivatives were synthesized from 3-bromo-4-chlorothieno[3,2-c]pyridine and cyclic amines, which by on Suzuki reaction with boronic acids converted to corresponding 3-arylthieno[3,2-c]pyridine. Substituent R3 has predominant effect on fluorescence properties of thienopyridines. However, the electron donor amine at C4 has no effect on fluorescence properties of thienopyridines

     

Theoretical and Experimental Study of the Diffraction Intensity of Gradient Refractive-Index Lenses

We develop the wave-optics approach for calculating the diffraction distribution of gradient refractiveindex lenses and observing the diffraction pattern of gradient refractive-index lenses in the experiments. The results of our calculation are in good agreement with the experimental results obtained. We show that the diffraction can be regarded as a method to check the quality of the refractive-index distributions of gradient refractive-index lenses.     

The Dynamics of Power laws: Fitness and Aging in Preferential Attachment Trees

Continuous-time branching processes describe the evolution of a population whose individuals generate a random number of children according to a birth process. Such branching processes can be used to understand preferential attachment models in which the birth rates are linear functions. We are motivated by citation networks, where power-law citation counts are observed as well as aging in the citation patterns. To model this, we introduce fitness and age-dependence in these birth processes. The multiplicative fitness moderates the rate at which children are born, while the aging is integrable, so that individuals receives a finite number of children in their lifetime. We show the existence of a limiting degree distribution for such processes. In the preferential attachment case, where fitness and aging are absent, this limiting degree distribution is known to have power-law tails. We show that the limiting degree distribution has exponential tails for bounded fitnesses in the presence of integrable aging, while the power-law tail is restored when integrable aging is combined with fitness with unbounded support with at most exponential tails. In the absence of integrable aging, such processes are explosive.     

A remark on analytic Fredholm alternative

We apply a recent result of Borichev–Golinskii–Kupin on the Blaschke-type conditions for zeros of analytic functions on the complex plane with a cut along the positive semi-axis to the problem of the eigenvalues distribution of the Fredholm-type analytic operator-valued functions.